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Alphabetical Index of Polytopes

Total count of actually available polytopes: 4836
Total count of contained incidence matrices: 11498
Acronyms and some of the names are due to Jonathan Bowers.

Index is also available indimensionally sorted order.Parts of this index - as far as circumradii are explicitly given - are also available in an (accordingly)numerically sorted order.

0...9 -A -B -C -D -E -F -G -H -I -J -K -L -M -N -O -P -Q -R -S -T -U -V -W -X -Y -Z



AcronymDim.NameCircumradius

0 ... 9

(2,2n)-pap4Ddyad - 2n-gon prismantiprismoid, s2s2s-2n-x, edge-alternatedsquare - 4n-gon duoprism...
(n,2m)-pap4Dn-gon - 2m-gon prismantiprismoid, s-n-s-2-s-2m-x, edge-alternated2n-gon - 4m-gon duoprism...
(N,M)-dafupap7D(N,M)-duoantifastegiaprismatic alterprism,(N,M)-duoantifastegiaprism atop lacing-ortho(N,M)-duoantifastegiaprism...
(n,m-ap)-dip5Dn-gon - m-antiprism - duoprismsqrt[1/(4 sin2(π/n))+(3-2 cos(π/m))/(8-8 cos(π/m))]
(n/d, m/b)-dow5Dn/d-grammal m/b-grammal disphenoid, n/d-grammal m/b-grammal duopyramid, {n/d} || perp {m/b}sqrt[1+1/(4 sin2(π d/n))]+1/(4 sin2(π b7m))/2
(n/d,m/b)-gybef5D(n/d,m/b)-gyrobifastegium, {n/d} atop(n/d,m/b)-duoprism atop perpendicular {m/b}...
..., 02,1,1,15DhyperbolicGosset pentacomb 02,1,1,11.732051i
..., 03,1,1,16DhyperbolicGosset hexacomb 03,1,1,11.414214i
..., 03,2,27DhyperbolicGosset heptacomb 03,2,22.449490i
...4Dmono-augmented trigonalmibdi-laced wedge...
10,n-dip4Ddecagon - n-gon duoprismsqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))]
...2Dhyperbolic [10,8,4,6] tiling with tetragonal Coxeter domain
..., 10Y4-8T-04Dparallellyoct dissectedoctet
..., 10Y4-8T-1-alt4Dalternating staggered 1×60°-gyrated10Y4-8T-0
..., 10Y4-8T-1-hel4Dhelical staggered 1×60°-gyrated10Y4-8T-0
..., 10Y4-8T-2-alt4Dalternating staggered 2×60°-gyrated10Y4-8T-0
..., 10Y4-8T-2-hel4Dhelical staggered 2×60°-gyrated10Y4-8T-0
..., 10Y4-8T-34D3×60°-gyrated10Y4-8T-0,trat-mirrored10Y4-8T-0
12,n-dip4Ddodecagon - n-gon duoprismsqrt[2+sqrt(3)+1/(4 sin2(π/n))]
...3Dtriangle hecatonicosahedron
...3Ddodeca-augmented rhombicuboctahedron
...3Dexternalblend of 12raded-1-10-5-5edge facetings
...3D12S-24R-6O polyhedron withinquitco's army1.062393
...4D(1,4)-expandedbited...
...3Dt16-r12,Stott contraction oft16-s12-r12-h4...
...3Dt16-s12-r12-h4,Stott expansion oft16-r12...
...4D1/10-luna ofhexacosachoron1.618034
..., 11,1,1,15Dhyperbolichexachoric-tetracomb pentacomb, hyperbolicGosset pentacomb 11,1,1,10i
..., 11,1,1,1,16DhyperbolicGosset hexacomb 11,1,1,1,10.25
..., 12,1,15DhyperbolicGosset pentacomb 12,1,10.707107i
..., 13,1,16DhyperbolicGosset hexacomb 13,1,10.707107i
..., 14,38DhyperbolicGosset octacomb 14,31.5i
..., 15,39DhyperbolicGosset enneacomb 15,31.118034i
..., 16,29DhyperbolicGosset enneacomb 16,22.236068i
...3Dcomplex polygonx2-4-or prism,complex polyhedronx2   x2-4-or
2,n-dap4Ddigon - n-gon duoantiprism, hemiatedsquare - 2n-gon duoprismsqrt[A2/2+B2/(4 sin2(π/2n))]
...4DShephard's3-generalised hexadecachoron,complex polychoronx2-3-o2-3-o2-4-o3, β34
...4DShephard's4-generalised hexadecachoron,complex polychoronx2-3-o2-3-o2-4-o4, β44
...4DShephard's5-generalised hexadecachoron,complex polychoronx2-3-o2-3-o2-4-o5, β54
...4DShephard'sp-generalised hexadecachoron,complex polychoronx2-3-o2-3-o2-4-op, βp4
...3DShephard's3-generalised octahedron,complex polyhedronx2-3-o2-4-o3, β330.707107
...3DShephard's4-generalised octahedron,complex polyhedronx2-3-o2-4-o4, β430.707107
...3DShephard's5-generalised octahedron,complex polyhedronx2-3-o2-4-o5, β530.707107
...3DShephard'sp-generalised octahedron,complex polyhedronx2-3-o2-4-op, βp30.707107
...3DDouble Hessian polyhedron,complex polyhedronx2-4-o3-3-o31
...2Dcomplex honeycombx2-4-o4-3-o4
...2Dcomplex honeycombx2-4-op-4-o2,complex honeycombop-4-x2-4-op
...3Dexternalblend of 20trippescus
...3D24 face equihedral toroid
...3Dt24-s6-24r,Stott contraction oft32-s24-r24-o6...
...3Dt24-s6-n82.431352
...4D2affic (?)1.414214
...4D2affidhi (?)2.236068
...3D2cho (?)1
...3D2co (?)1
...3D2co+16{3} (?)1
...4D2cont (?)3.414214
...3D2cube (?)0.866025
...4D2cuhsquah (?)
...5D2dah (?)0.790569
...4D2deca (?)1.414214
...3D2did (?)1
...3D2ditdid+5cube (?)0.866025
...4D2dittafady (?)1.414214
...3D2doe (?)1.401259
...4D2ex (?)1.618034
...4D2ex+fix (?)1.618034
...4D2firgaghi (?)1.070466
...4D2firgogishi (?)0.661585
...6D2firl (?)0.845154
...4D2firp (?)0.774597
...4D2firsashi (?)2.802517
...5D2firx (?)0.816497
...4D2fix (?)1.618034
...4D2frico (?)1.732051
...4D2fry (?)4.534568
...3D2gad (?)0.951057
...3D2gad+ike (?)0.951057
...4D2gadtifady (?)0.874032
...4D2gaghi (?)1
...4D2gaghi+2paphacki (?)1
...4D2gahi (?)1.618034
...4D2garpop+20{6/2}1.183216
...4D2gashi (?)0.618034
...4D2gax (?)0.618034
...3D2geihid (?)0.618034
...3D2gid (?)0.618034
...4D2gidditdy (?)1.732051
...4D2gidditpix+2dithix (?)1.732051
...3D2gidhei (?)1
...3D2gidhid (?)0.618034
...3D2gidtid+5cube (?)0.866025
...4D2gifdahihox (?)1
...3D2gike (?)0.587785
...3D2gike+sissid (?)0.587785
...4D2gippapivady (?)0.726543
...4D2giprapivady (?)1.902113
...4D2gishi (?)0.618034
...3D2gissid (?)0.535233
...4D2gitphi (?)0.874032
...4D2gofix (?)0.618034
...4D2gogishi (?)0.540182
...4D2gohi (?)1.618034
...4D2grahi (?)11.252107
...4D2grico (?)4.299451
...4D2grip (?)1.843909
...4D2grit (?)3.005916
...4D2grix (?)9.124101
...7D2guhsa (?)0.707107
...5D2hehad (?)0.707107
...4D2hex+8oct (?)0.707107
...2D2hexat (?)
...4D2hi (?)3.702459
...2D2hoha (?)
...5D2howoh (?)1.732051
...4D2huhoh+3tes+8co (?)1
...4D2ico (?)1
...4D2ico+2gico (?)1
...4D2ico+48{4}+128{3} (?)1
...3D2id (?)1.618034
...3D2id+40{3} (?)1.618034
...4D2iddip (?)1.693527
...3D2ike (?)0.951057
...3D2ike+4gad (?)0.951057
...3D2ike+gad (?)0.951057
...6D2kaje (?)0.816497
2n,2m-dip4D2n-gonal - 2m-gonal duoprismsqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/2m))]
2n,m-dip4D2n-gonal - m-gonal duoprismsqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/m))]
2n-p3D2n-gonal prismsqrt[1/4+1/(4 sin2(π/2n))]
2n/2-p3D2n-gonal prism of winding number 2sqrt[1/4+1/(4 sin2(π/n))]
2n/d-p3D2n/d-prism, 2n-prism with winding number dsqrt[1/4+1/(4 sin2(π d/2n))]
...3D2oct (?)0.707107
...3D2oct+12{4} (?)0.707107
...3D2oct+6{4} (?)0.707107
...3D2oct+8{3} (?)0.707107
...4D2oh (?)1
...3Dblend of 2pentagonal antiprisms, pair ofpentagonal butterfly wedges0.951057
...4D2papvixhi (?)1.902113
...4D2pen (?)0.632456
...3D2pip (?), decagonal prism with winding number 20.986715
...4D2prahi (?)8.278950
...4D2prapvixhi (?)1.175571
...4D2prico (?)3.498949
...4D2prip (?)1.612452
...4D2prit (?)2.370932
...4D2prix (?)9.744610
...4D2proh (?)2.613126
...4D2quiphi (?)0.726543
...3D2quitgissid (?)0.657550
...3D2quith (?)0.579471
...3D2quitsissid (?)0.852911
...3D2raded (?)1.322876
...4D2rahi (?)4.534568
...4D2rahi+2400tet (?)4.534568
...4D2rap (?)0.774597
...4D2rap+20tet (?)0.774597
...4D2ratho (?)1
...5D2rhohid (?)1
...4D2rico (?)1.732051
...4D2rico+64{6}+128{3} (?)1.732051
...4D2rico+64{6}+192{3} (?)1.732051
...4D2ridditdy (?)1.732051
...5D2rinhit (?)1
...4D2rit+64tet (?)1.224745
...2D2srothat (?)
...4D2rox (?)3.077684
...4D2rox+1440{5}+2400{3} (?)3.077684
...4D2rox+sophi (?)3.077684
...4D2sadtifady (?)2.288246
...3D2seihid (?)1.618034
...4D2sidditdy (?)1.732051
...4D2sidditpix+2dithix (?)1.732051
...3D2sidhei (?)1
...3D2sidhid (?)1.618034
...3D2sidtid+5cube (?)0.866025
...4D2sifdahihox (?)1
...3D2sirco (?)1.398966
...4D2sishi (?)1
...4D2sishi+2paphicki (?)1
...3D2sissid (?)0.587785
...3D2sissid+4gike (?)0.587785
...3D2sissid+gike (?)0.587785
...4D2sitphi (?)2.288246
...4D2sophi (?)3.077684
2sophip5D2sophi prism3.118034
...4D2spapivady (?)1.175571
...4D2sprapivady (?)3.077684
...4D2srahi (?)6.735034
...4D2srahi+1440{10}+4800{3} (?)6.735034
...4D2srahi+2400trip (?)6.735034
...4D2srico (?)2.613126
...4D2srico+144{8}+576{3} (?)2.613126
...4D2srico+192trip (?)2.613126
...3D2srid (?)2.232951
...4D2srip (?)1.183216
...4D2srip+20{6}+40{3} (?)1.183216
...4D2srip+20{6}+60{3} (?)1.183216
...4D2srip+20trip (?)1.183216
...4D2srit (?)1.847759
...4D2srit+48{8}+128{3} (?)1.847759
...4D2srit+64trip (?)1.847759
...4D2srix (?)6.073594
...4D2srix+2400{6}+4800{3} (?)6.073594
...4D2srix+2400{6}+7200{3} (?)6.073594
...4D2tah (?)2.121320
...4D2tes (?)1
...3D2tet (?)0.612372
...3D2thah (?)0.707107
...4D2thahp (?)0.866025
...2D2that (?)
...2D2that+∞{3} (?)
...4D2thex (?)1.581139
...4D2tho (?)0.707107
...4D2tho+24{4} (?)0.707107
...6D2thox (?)0.707107
...3D2ti (?)2.478019
...3D2tic (?)1.778824
...3D2tid (?)2.969449
...3D2tiggy (?)1.053292
...3D2tigid (?)1.876844
...4D2titho (?)1.581139
...2D2toxat (?)
...3D2trip (?), hexagonal prism with winding number 20.763763
...3D2tut (?)1.172604
...4D2xhi (?)7.579634
...4D2/10-luna ofhexacosachoron1.618034
..., 23,27DhyperbolicGosset heptacomb 23,20.577350i
..., 24,28DhyperbolicGosset octacomb 24,20.288675i
..., 26,19DhyperbolicGosset enneacomb 26,11.414214i
...3Dcomplex polyhedronx3   x3-3-o30.912871
3,n-dip, K-4.1754Dtriangle - n-gon duoprism, n-gon -n-prismatic wedgesqrt[1/3+1/(4 sin2(π/n))]
3,n-dippip5Dtriangle - n-gon duoprismatic prismsqrt[7/12+1/(4 sin2(π/n))]
...3DHessian polyhedron,complex polyhedronx3-3-o3-3-o30.816497
...4DWitting polychoron,complex polychoronx3-3-o3-3-o3-3-o31
...3DRectified Hessian polyhedron,complex polyhedronx3-3-o3-4-o21
...2Dcomplex honeycombx3-3-o3-4-o3
...3Dcomplex polyhedronx3-3-o3 || o3-3-x3,vertex figure ofx3-3-o3-3-o3-3-x30.790569
...3DShephard's3-generalised cube,complex polyhedronx3-4-o2-3-o2, γ331
...4DShephard's3-generalised tesseract,complex polychoronx3-4-o2-3-o2-3-o2, γ34
...2Dcomplex honeycombx3-4-o3-3-o3
...3Dhyperbolic [3,4,3,4,4,4] tiling
3-gybef5Dtriangle-gyrobifastegium, triangle atoptes atop perpendicular triangle...
...4Dgeneral variant oftriddapsqrt[(a2+b2)/3]
...3Dtriaconta-augmented rhombicosidodeahedron...
...3D32 face equihedral toroid
...3Dt32-s24-r24-o6,Stott expansion oft24-s6-24r...
...2Dhyperbolic [(33,4)4] tiling
...3Dtriangle triacontahexahedron
..., {3} || gybef4D{3} ||gyrobifastegium...
...3D3doe (?)1.401259
...4D3doe-1pap-10mibdi-10teddi-diminishedex1.618034
...4D3ex+2fix+gaghi (?)1.618034
...4D3ex+fix (?)1.618034
...3D3gidtid (?)0.866025
...3D3gissid (?)0.535233
...3D3ike+3gad (?), 3cid (?)0.951057
...3D3ike+gad (?)0.951057
...3D3oct+6{4} (?)0.707107
...4D3pen (?)0.632456
..., 3Q3-S3-2P6-2P3-gyro3Dparallellythat dissected, elongatedrich
..., 3Q3-S3-2P6-2P3-ortho3Dparallellythat dissected, elongatedgyrich
..., 3Q4-T-2P8-P44Dparallellysirco dissectedratoh
...4D3rasishi (?)2.802517
...3D3sidtid (?)0.866025
...4D3sishi (?)0.809017
...3D3sissid+gike (?)0.587785
...4Dthreesquafblend, "thah-squares star" atopcube0.879465
...4Dthreesquippypblend, "coord-axes edge star" atopcube0.866025
...3D3tet (?)0.612372
...4Dthreetisdipblend, "coord-planes squares star" atopcube0.912871
...4D3/10-luna ofhexacosachoron1.618034
..., 31,1,16Dhyperbolic (order 3) hexacontitetrapetic hexacomb, hyperbolicGosset hexacomb 31,1,10.5
..., 32,27Dhyperbolic hecatonicosihexapentacosiheptacontihexaexic heptacomb, hyperbolicGosset heptacomb 32,20i
..., 34,18DhyperbolicGosset octacomb 34,10.5i
..., 35,19DhyperbolicGosset enneacomb 35,10i
4,2n-dip4Dsquare - 2n-gon duoprismsqrt[1/2+1/(4 sin2(π/2n))]
4,2n/d-dip4Dsquare - 2n/d-gram duoprismsqrt[1/2+1/(4 sin2(πd/2n))]
4,n,m-tip6Dsquare - n-gon - m-gon - triprismsqrt[1/2+1/(4 sin2(π/n))+1/(4 sin2(π/m))]
4,n,n-tip6Dsquare - n-gon - n-gon - triprismsqrt[1/2+1/(2 sin2(π/n))]
4,n-dip, K-4.1774Dsquare - n-gonal duoprismsqrt[1/2+1/(4 sin2(π/n))]
4,n/d-dip4Dsquare - n/d-gramal duoprismsqrt[1/2+1/(4 sin2(πd/n))]
...2Dcomplex honeycombx4-3-o4-3-o4
...2Dcomplex honeycombx4-3-o4-4-o2,complex honeycombo4-3-x4-3-o4
...3DShephard's4-generalised cube,complex polyhedronx4-4-o2-3-o2, γ431.224745
...4DShephard's4-generalised tesseract,complex polychoronx4-4-o2-3-o2-3-o2, γ44
...3Dhyperbolic [4,4,6,6] tiling with tetragonal Coxeter domain
...2Dhyperbolic [4,6,6,∞] tiling with tetragonal Coxeter domain0.707107i
4-gybef5Dsquare-gyrobifastegium, square atoptes atop perpendicular square...
...4Dtetracontadisdiminishedex1.618034
...4Dtetracontadisdiminishedsidpixhi5.236068
...4D4D corner hypercubera1
..., {4} || perp {4}5D(degenerate) square atop fully orthogonal square, square disphenoid∞   i.e. flat in euclidean space
...4D4hi3.702459
...3D4ike+2gad (?)0.951057
...3D4ike+gad (?)0.951057
...3D4oct (?)0.707107
...4D4pen0.632456
...4D4pen+160{3} (?)0.632456
...3D4sissid+2gike (?)0.587785
...3D4tet (?)0.612372
...3D4thah (?)0.707107
...3Dfourtripblend, threetutripblend0.763763
...4D4/10-luna ofhexacosachoron1.618034
..., 42,28Dhyperbolic dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zettic octacomb, hyperbolicGosset octacomb 42,20.5
..., 43,18DhyperbolicGosset octacomb 43,10i
...3DLeonardo polyhedron of type {4,5;19}
...3DLeonardo polyhedron of type {4,5;31}
5,n-dip4Dpentagon - n-gon duoprismsqrt[(5+sqrt(5))/10+1/(4 sin2(π/n))]
5,n-dippip5Dpentagon - n-gon duoprismatic prismsqrt[(15+2 sqrt(5))/20+1/(4 sin2(π/n))]
...3DShephard's5-generalised cube,complex polyhedronx5-4-o2-3-o2, γ531.473370
...4DShephard's5-generalised tesseract,complex polychoronx5-4-o2-3-o2-3-o2, γ54
..., {5} || perp {5/2}5D(degenerate) pentagon atop fully perpendicular pentagram∞   i.e. flat in euclidean space
...3Dbiformcompound of 5dodecahedra1.401259
..., K-4.1464Dpentagon -pentagonal-rotunda wedge, {5} ||pero3.077684
...4Douter pentadiminished 2/10-luna ofhexacosachoron1.618034
..., {5} || gyro pedip5D(degenerate) pentagon atop gyratedpedip∞   i.e. flat in euclidean space
...3D5ike+gad (?)0.951057
..., 5Y4-4T-4P43Delongated10Y4-8T-0
..., 5Y4-4T-6P3-sq-para3Dpara-staggered shear-elongated10Y4-8T-0
..., 5Y4-4T-6P3-sq-skew3Dskew-staggered shear-elongated10Y4-8T-0
..., 5Y4-4T-6P3-tri-04Dtrat-elongated10Y4-8T-0
..., 5Y4-4T-6P3-tri-1-alt4Dtrat-elongated10Y4-8T-1-alt
..., 5Y4-4T-6P3-tri-1-hel4Dtrat-elongated10Y4-8T-1-hel
..., 5Y4-4T-6P3-tri-2-alt4Dtrat-elongated10Y4-8T-2-alt
..., 5Y4-4T-6P3-tri-2-hel4Dtrat-elongated10Y4-8T-2-hel
..., 5Y4-4T-6P3-tri-34Dtrat-elongated10Y4-8T-3
..., 53,19DhyperbolicGosset enneacomb 53,10.5
...3DLeonardo polyhedron of type {5,4;13}
6,n-dip4Dhexagon - n-gonal duoprismsqrt[1+1/(4 sin2(π/n))]
...3Dtriformblend of 6pentagonal prisms0.986715
...3Dt60-r60-p12,Stott contraction oft80-s60-r60-d12...
...3D6doe (?)1.401259
...3D6gissid (?)0.535233
...3Dsquippy-teddi-G3 toroid...
...4D6pen0.632456
..., 6Q3-2S3-gyro3Dparallellythat dissectedrich
..., 6Q3-2S3-ortho3D(un)gyrated6Q3-2S3-gyro
..., 6Q4-2T4Dparallellysquobcu dissectedpacratoh
...4D6sishi (?)1
...4D6tes (?)1
...3D6tet (?)0.612372
..., 62,19DhyperbolicGosset enneacomb 62,10i
...4Dgeneral 7-2-stepprismsqrt(A2+B2)
...4Dheptadiminished2/10-luna of ex bidiminishedinner pentadiminished 2/10-luna of ex
8,n-dip4Doctagon - n-gonal duoprismsqrt[(2+sqrt(2))/2+1/(4 sin2(π/n))]
...3Dt80-s60-r60-d12,Stott expansion oft60-r60-p12...

A

...3Da3b3c, general variation oftruncated octahedronsqrt[(3a2+4b2+3c2+4ab+2ac+4bc)/8]
...3Da3b4c, general variation ofgreat rhombicuboctahedronsqrt[2a2+4b2+3c2+4ab+(2ac+4bc)sqrt(2)]/2
...3Da3b5c, general variation ofgreat rhombicosidodecahedronsqrt[(f+2)a2+4(f+1)ab+2(2f+1)ac+4(f+1)b2+4(2f+1)bc+3(f+1)c2]/2
...4Dtriangular duoexpandoprismsqrt[(a2+3b2)/3]
...4Dterminally edge-beveledhexadecachoron
...4Dedge-beveledhexadecachoron
...4Dtetracontoctachoron-derived Gévay polychoron...
addasi3Daltered disnub icosahedron,compound of 20oct (butnotdasi)0.707107
afdec4Dantifrustic distetracontoctachoron1.414214
affic4Dantifrustary tetracontoctachoron1.414214
affidhi4Dantifrustary dishecatonicosachoron2.236068
affip4Dantifustric prismatochoron,compound of 16hiddip1.414214
affixthi4Dantifrustic hexacositrishecatonicosachoron2.236068
afpox (old: affopix)4Dantifustric prismatohexacosachoron,compound of 60gippid2.236068
ahach3Dhyperbolic alternated order 6cubical honeycomb, hyperbolic snub order 6 cubical honeycomb0i
ahexah3Dhyperbolic alternatedhexagonal-tiling honeycomb0.816497i
...3Dgeneraltetrahedral-octahedral honeycomb variant ao3bo3oa3ob3*a&#zc (butnotao3bo3ob3oa3*a&#zc)
...3Dgeneraltetrahedral-octahedral honeycomb variant ao3bo3ob3oa3*a&#zc (butnotao3bo3oa3ob3*a&#zc)
...4Daoc3ddd3cao *b3oca&#ze, general variant ofprismatorhombisnub icositetrachoronsqrt[(a2+ac+c2+2ad+2cd+2d2)/2]
...4Daoc3ooo3cao *b3oca&#zdsqrt[(a2+ac+c2)/2]
apech3Dhyperbolic alternated order 5 cubical honeycomb0.393076i
aphexah3Dhyperbolic alternated order 5hexagonal-tiling honeycomb0.220528i
apid (alt.: bamid)4Dantiprismatodecachoron, biambodecachoron, triangle based biambodecachoron0.774597
arie3Dantirhombicosicosahedron,compound of 5co1
arsdod depabdirox4Daround-symmetrical dodecadiminishing of deep parabidiminishedrox3.077684
arse aurap4Daround-symmetrically expandedaugmented rectified pentachoron
arse biscrahi4Dbistraticicosidodecahedron-first subsegment ofsmall rhombihexacosachoron, around-symmetrically expandedbiscrahi6.073594
arspabd biscrox4Daround-symmetrically parabidiminished bistraticicosahedron-first cap ofrectified hexacosachoron3.077684
arsque biscrighi4Daround-symmetrically quasi-expanded bistraticdodecadodecahedron-first cap ofrectified great hecatonicosachoron1.662508
arsted biscrox4Daround-symmetrically tridiminished bistraticicosahedron-first cap ofrectified hexacosachoron3.077684
arsted diddidex4Daround-symmetrical tridiminishing of (axial) duo-disdodeca-icosa-diminishedhexacosachoron1.618034
ashexah3Dhyperbolic alternated order 4hexagonal-tiling honeycomb0.408248i
asquat2Dhyperbolic order ∞ square tiling0i
atich3Dalternatedly truncated cubic honeycomb
aubautipip4Daugmentedbiaugmented-triangular-prism prism
aud, J583Daugmented dodecahedron
auhip, J543Daugmented hexagonal prism
aupip, J523Daugmented pentagonal prism
aurap4Daugmented rectified pentachoron
auteddi, J643Daugmented tridiminished icosahedron
auteddipe4Daugmented-tridiminished-icosahedron prism...
autepe4Daugmentedtetrahedral prism
autic, J663Daugmented truncated cube
autid, J683Daugmented truncated dodecahedron
autip, J493Daugmented triangular prism
autipip4Daugmented-triangular-prism prism...
autodip4Daugmented3-8-duoprism...
autpen4Daugmentedtruncated pentachoron...
autut, J653Daugmented truncated tetrahedron
auwaco, J873Daugmented sphenocorona
ax (old: hexe)6Dhexeract, dodecapeton, 6Dmeasure-polytope (γ6), geoex(id)1.224745
...3DWaterman polyhedron number 8 wrt. face-centered cubiclattice A3 centered at a lattice point
axh6Dhexeractic hexacomb, 6Dhypercubical honeycomb (δ6)
...4DAxoFFxoox3oFFxofoxo xofofxFof3oxofxfoFf&#zx
...4DAxoFFxxo3oFFxofxx xofofxFo3oxofxfoF&#zx
azap2Dapeirogonal antiprism
azat2Dhyperbolic order 3 apeirogonal tiling, hyperbolic order 3 horocyclic tiling, hyperbolic truncated order ∞ horocyclic tiling0.866025i
azazat2Dhyperbolic order ∞ apeirogonal tiling, hyperbolic order ∞ horocyclic tiling0i
aze1Dapeirogon, infinitogon, horogon (esp. when used as tile inhyperbolic geometry)
azip2Dapeirogonal prism
aztrat2Dhyperbolic order ∞ triangular tiling0i

B

bachid5Dbiprismaticellihemidodecateron1
bacox5Dbiprismatocellihexateron1
bad5Dbiprismatododecateron0.866025
...4Dvertex figure ofbiprismatododecateron0.816497
badhidy (old: buthi)4Dblendic dishecatonicosa-dishecatonicosachoron,compound oftigaghi andquit sishi2
badohi4Dblendic dishecatonicosachoron2
bagydrid, J793Dbigyrate diminished rhombicosidodecahedron2.232951
bamic (old: apic)4Dbiambotetracontoctachoron, antiprismatotetracontoctachoron, triangle based biambotetracontoctachoron1.732051
bamich3Dbiambocubic honeycomb
bapril6Dbiprismatorhombatedheptapeton, biruncitruncated heptapeton2.203893
bark8Dbirectified diacosipentacontahexazetton, equatorial cross-section ofrek-firstbrav1.224745
barm (old: scram, bram, remak, kram)6Dbirectifiedpentacontitetrapeton, (small centrorhombated pentacontitetrapeton)2.449490
...6Disomorph ofbirectified pentacontitetrapeton0.816497
barn9Dbirectified enneract, birectified octadecayotton,Gosset polytope 06,1,11.870829
barz (old: drhio)7Dbirectified hecatonicosoctaexon, equatorial cross-section ofrez-firstbark1.224745
batal6Dbitruncatedheptapeton1.647509
batch3Dbitruncated cubic honeycomb, truncated-octahedral honeycomb,Voronoi complex of body-centered cubic (bcc)lattice
batene8Dbitruncated enneazetton1.795055
baticot4Dbitruncated icositetrachoric tetracomb, small tetracontaoctachoric tetracomb
batitit4Dbitruncated tesseractic tetracomb
bato8Dbitruncatedocteract3.535534
bauautipip4Dbiaugmentedaugmented-triangular-prism prism...
bauco3Dbi-augmentedcuboctahedron, 4fold rhombohedron...
baucubaike4Dbi-augmentedcubaike
baudeca4Dbiaugmenteddecachoron
baupip, J533Dbiaugmented pentagonal prism
bautic, J673Dbiaugmented truncated cube
bautip, J503Dbiaugmented triangular prism
bautipip4Dbiaugmented-triangular-prism prism
...4DBAVFfxoo xFofxFVo3xxFxooxo5xooxFfoV&#zx
bay8Ddiacositetraconta-myriaheptachiliadiacosioctaconta-zetton, argyrozetton,Gosset polyzetton 24,11.414214
bayoh8Ddiacositetracont-myriaheptachiliadiacosioctaconta-zettic octacomb,Gosset octacomb 25,1
be8Doctadecazetton, enneaenneazetton, bi-enneazetton, quadritruncated enneazetton, equatorial cross-section of (vertex first) q-enne2
bend5Dbiprismatointercepted dodecateron0.866025
...4Dvertex figure ofbiprismatointercepted dodecateron0.816497
berlin (old: shabrilq)7Dbirectified pentacontihexahecatonicosihexaexon (small demibirhombated pentacontihexapentacosiheptacontihexaexon)3.570714
bersa (old: dars)7Dbirectified hepteract,Gosset polytope 04,1,11.581139
betsa7Dbitruncatedhepteract3.240370
bhidtex4Dbi-hecatonicosidiminishedtruncated hexacosichoron4.643523
...3Dcubically-diminisheddodecahedron, bi-tetrahedrally-diminisheddodecahedron1.401259
bichon (old: dubatch)4Dbicubical honeycomb, tetragonary disphenoidal honeycomb,bitruncated-cubical-honeycomb dual,Delone complex of body-centered cubiclattice A3*
bicont (old: ducont)4Dbitetracontoctachoron,tetracontoctachoron dual, bi-apiculatedicositetrachoron, tetradisphenoidal 288-cell1.306563
bicotoe6Dbi -(cuboctahedron, truncated octahedron)-duoprism1.870829
bicypdex (alt.: bicypaugap)4Dbi-cyclopentadiminishedhexacosachoron, bi-cyclopentaaugmentedgreat antiprism1.618034
bicypdrahi4D(bistratic) bi-cyclopentadiminishedrectified hecatonicosachoron4.534568
bicypdrox4D(bistratic) bi-cyclopentadiminishedrectified hexacosachoron3.077684
bicyte ausodip4Dbicyclotetraugmentedsquare-octagon duoprism...
bicyte gysrit4Dbicyclotetragyratedsmall rhombitesseract1.847759
bideca (old: dudeca)4Dbidecachoron,decachoron dual, bi-apiculatedpentachoron, 10-3-stepprism0.816497
bidex4Dbi-icositetradiminishedhexacosachoron1.618034
bidhin (alt.: octahex, tetalrap, tetaltet octtric)5Dbidiminishedhemipenteract,oct ||hex,tet || invertedrap, (tet,dualtet,oct)-trigonic0.790569
bidoctaco, {4} || co, K-4.284Dsquare atopcuboctahedron, bidiminishedoctaco, square firstrotunda ofcytau tes1
bidot5Dbidodecateron, triangular duotegmatic icosateron, triangular duotegmatic alterprism,dodecateron dual0.790569
bidrap, K-4.84Dbidiminishedrectified pentachoron, antiduowedge, square -tetrahedral wedge, digonal gyrobicupolaic ring, {4} ||tet, line || orthotrip0.774597
bidrappy5Dbidrap pyramid0.790569
bidrix5Dbidiminishedrectified hexateron0.816497
bidsid pixhi4Dbi-icositetra-diminishedsmall disprismatohexacosihecatonicosachoron5.236068
bidsrip4Dbidiminishedsmall rhombated pentachoron1.183216
bif8Ddiacositetracont-dischiliahectohexaconta-zetton, chrysozetton, Gosset polyzetton 14,22
bife6Dbitetradecapeton,tetradecapeton dual, 14-3-5 step prism0.774597
bifoh8Ddiacositetracont-dischiliahectohexaconta-zettic octacomb,Gosset octacomb 15,2
big dispox6Dbi-hexacontatetra (= g)-diminishedsmall-prismated-hexeract2.263033
bilbiro, J913Dbilunabirotunda
...4Dbilbiro wedge...
bimtec4Dbimesotruncatotetracontoctachoronsqrt[3a2+4ab sqrt(2)+3b2]
bimted (old: bimtid)4Dbimesotruncatodecachoronsqrt[(3a2+4ab+3b2)/5]
bimteth3Dbimesotruncatotetrahedral honeycomb
bimtich3Dbimesotruncatocubic honeycomb
bipach3Dbiprismatocubic honeycomb
bipec4Dbiprismatotetracontoctachoronsqrt[a2+ab sqrt(2)+b2]
biped4Dbiprismatodecachoronsqrt[(2a2+ab+2b2)/5]
bipgy srit4Dbipara(bi)gyratedsmall rhombitesseract, pseudo cantellated tesseract1.847759
birachach3Dhyperbolic birectified alternated order-6 cubic honeycomb, hyperbolic runcic order-6 cubic honeycomb1.168771i
birapech3Dhyperbolic birectified alternated order-5 cubic honeycomb, hyperbolic runcic order-5 cubic honeycomb1.507495i
birashexah3Dhyperbolic birectified alternated order 4hexagonal-tiling honeycomb0.934758i
birgax4Dbi-icositetra-replenished grand hexacosachoron0.618034
bisc sridtathi4Dbistraticdodecahedron-first cap ofsmall retroinverted ditetrahedronary trishecatonicosachoron2.288246
biscex4Dbistratic vertex-first cap ofhexacosachoron1.618034
bisch3Dbisnub cubic honeycomb
biscpoxic4Dbistratic vertex-first cap ofpoxic
biscrahi4Dbistraticicosidodecahedron-first cap ofrectified hecatonicosachoron4.534568
biscrighi4Dbistraticdodecadodecahedron-first cap ofrectified great hecatonicosachoron1.902113
biscrox4Dbistraticicosahedron-first cap ofrectified hexacosachoron3.077684
biscsrico4Dbistraticcuboctahedron-first cap ofsmall rhombated icositetrachoron2.613126
biscsrip4Dbistratictrip-cap ofsrip, {3}-diminishedsmall rhombated pentachoron1.183216
bitach4Dbitruncatocubic honeycomb,tegum sum of 2 inverted (x,y)-tichs
bitapech3Dhyperbolic bitruncated alternated order-5 cubic honeycomb, runcicantic order-5 cubic honeycomb2.850727i
bitapna4Dbitrigonal antiprismattic enenehexachoron,compound of 8ico inrico army,compound of 2kitapna1
bitdi3Dchiral Weimholt hexahedron, bitrigonally diminished icosahedron,vertex figure ofbidex0.951057
bitdoh (old: ciddoh)3Dhyperbolic bitruncated order 5 cubic honeycomb, hyperbolic bitruncated order 4 dodecahedral honeycomb, hyperbolic cubic-dodecahedral honeycomb2.443795i
bitec (old: sidwapic)4Dbitruncatotetracontoctachoron, snub disphenic antiprismatotetracontoctachoron, general variant of hull oftastic,tegum sum of 2 inverted (x,y)-ticoessqrt(3y2+3y+1)
bited (old: sidwapid)4Dbitruncatodecachoron, snub disphenic antiprismatodecachoron, general variant of hull oftisted,tegum sum of 2 inverted (x,y)-tipssqrt[(3y2+3y+2)/5]
biteday9Dbitruncated decayotton1.802776
bitefa4Dbitegmic hecatontetracontatetrachoron,compound of 12ico inspic army,compound of 2kitefa1
bitem (old: gacram, botam, kobtam)6Dbitruncatedpentacontitetrapeton, (great centrorhombated pentacontitetrapeton, heptacontidia-bitruncated pentacontitetrapeton)4.123106
bitettut (alt.: pabex gee)6Dbi -(tetrahedron, truncated tetrahedron)-duoprism,partially bi-expandedhexacontitetrapeton1.322876
bithi4Dblendic trishecatonicosachoron2
bithit4Dbitruncated hexadecachoric tetracomb, bitruncated demitesseractic tetracomb, runcicantic tesseractic tetracomb
bithon3Dbitetrahedral honeycomb
...4DbitruncatedWitting polychoron,complex polychorono3-3-x3-3-x3-3-o3
...4Dbitruncatedgeneralized Shephard tesseract, bitruncatedgeneralized Shephard hexadecachoron,complex polychoronop-4-x2-3-x2-3-o2
bittin5Dbitruncatedpenteract2.549510
bittit5Dbitruncatedtriacontiditeron, Voronoi cell oflattice D5*2.121320
bittita sibrant6Dbitruncated triacontadipeton atopsmall birhombated penteractitriacontiditeron,sart-first subsegment ofsmall birhombated hexacontitetrapeton2.236068
bittix (old: dittox)5Dbitruncatedhexateron1.554563
bittixa (old: bittixalbittix)6Dbitruncated-hexateron alterprism,bitruncated-hexateron atop invertedbitruncated-hexateron, equatorial segment ofrectified hexeract1.581139
bittoc7Dbitruncated octaexon1.713914
bobipyr3Dbowtie bipyramid, crossed-square bipyramid, bowtie (line-)tegum0.707107
bodnit5Dbi-octa-diminishedpenteractitriacontiditeron1.224745
boprag6Dbiprismatorhombatedhexacontitetrapeton, biruncitruncatedhexeract3.674235
boprax6Dbiprismatorhombatedhexeract, biruncitruncated hexacross3.464102
borfy8Dbirectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t2(41,2)2.449490
bostarpglassdit5Dbowtie -pentagrammic-retroprismatic-hourglass duotegum0.707107
botag6Dbitruncatedhexacontitetrapeton, bitruncated hexacross2.121320
botajik6Dbitruncatedicosiheptaheptacontidipeton2.943920
botaz7Dbitruncated hecatonicosoctaexon, bitruncated heptacross2.121320
botlaq7Dbitruncated pentacontihexapentacosiheptacontihexaexon4.123106
botnaq7Dtruncated hecatonicosihexapentacosiheptacontihexaexon3.278719
botox6Dbitruncatedhexeract2.915476
brade10Dbirectified dekeract, birectified icosaxennon,Gosset polytope 07,1,12
brag (old: dric)6Dbirectifiedhexacontitetrapeton, Voronoi cell oflattice D6*, equatorial cross-section ofrag-firstbarz1.224745
bragabrox7Dbrag atopbrox,brag-firstrotunda ofsez1.414214
bragasochax7Dbrag atopsochax, 2nd subsegment oflin inhax-first orientation1.322876
brake10Dbirectified chilliaicositetraxennon1.224745
branq (old: dranq)7Dbirectified hecatonicosihexapentacosiheptacontihexaexon1.936492
brav9Dbirectified pentacosidodecayotton, equatorial cross-section ofriv-firstbrake1.224745
braxh6Dbirectified hexeractic honeycomb
breday9Dbirectified decayotton,Gosset polytope 06,2,vertex figure of hyperbolic16,21.024695
brena9D(degenerate)birectified enneazettonalterprism∞   i.e. flat in euclidean space
brene8Dbirectified enneazetton,Gosset polytope 05,21
brewahen5Dbiretrosphenary demipenteract2.236068
bricot4Dbirectified icositetrachoric tetracomb, birectified demitesseractic tetracomb, runcic tesseractic tetracomb
bril (old: driss, alt.: rixadot)6Dbirectifiedheptapeton,rectified hexateron atopdodecateron,vertex figure oflin,Gosset polytope 03,20.925820
brilalspil7Dbril atop invertedspil1.322876
brilastaf7Dbril atopstaf,hop-first subsegment oflaq1
brillip7Dbirectified - heptapeton prism1.052209
brilpy7Dbirectified-heptapetonal pyramid, vertex pyramid ofpentacontihexahecatonicosihexaexon1.322876
brinoh5Dbirectified penteractic pentacomb
bro8Dbirectified octeract, birectified hexadecazetton,Gosset polytopes 05,1,11.732051
broc (old: droc)7Dbirectified octaexon, duorectified octaexon,vertex figure ofbif,Gosset polytope 04,20.968246
broca (old: brocalbroc)8Dbroc alterprism,broc atop invertedbroc, central segment ofhocto1
brox (old: drax)6Dbirectifiedhexeract,Gosset polytope 03,1,1, equatorial cross-section ofbrag-firstsez1.414214
broxa sophax7Dbrox atopsophax,hax-first subsegment ofrolaq1.732051
bru10Dbirectified hendecaxennon,Gosset polytope 07,21.044466
buffy8Ddiacositetracont-dischiliahectohexacont-myriaheptachiliadiacosioctaconta-zetton, rectifiedbif:  t1(12,4), birectifiedbay:  t2(21,4), tetrarectifiedfy:  t4(41,2),Gosset polytope 04,2,13.872983
...4DBxxFxfofx3oooxxxFFF3xBxfFxxof *b3xxBxfFfxo&#zx

C

...2Dc01 of hyperbolic[10,8,4,6] tiling with tetragonal Coxeter domain*
...2Dc0 of hyperbolic[10,8,4,6] tiling with tetragonal Coxeter domain*
cabbix5Dcellibiprismatohexateron0.866025
...4Dvertex figure ofcellibiprismatohexateron0.816497
cabisch3Dcantic bisnub cubic honeycomb
cadditradid3Dcomplex (ditrigonary) rhombidodecadodecahedron0.866025
caddix5Dcellidishexateron0.866025
...4Dvertex figure ofcellidishexateron0.816497
cagoraht (old: gicaricot)4Dcelligreatorhombatedhexadecachoric tetracomb (great cellirhombated icositetrachoric tetracomb), stericantitruncated hexadecachoric tetracomb
cagorg (old: gacorg)6Dcelligreatorhombihexacontitetrapeton, (old: great cellirhombated hexacontatetrapeton), stericantitruncated hexacontatetrapeton3.937004
cagorx (old: gacorx)6Dcelligreatorhombatedhexeract, (old: great cellirhombated hexeract), stericantitruncated dodecapeton4.772649
cagral (old: gacral)6Dcelligreatorhombatedheptapeton, stericantitruncated heptapeton2.618615
cagratit (old: gicartit)4Dcelligreatorhombated tesseractic tetracomb (great cellirhombated tesseractic tetracomb), great rhombitesseractic-prismatotesseractic tetracomb, stericantitruncated tesseractic tetracomb
cagricot (old: gicaroht)4Dcelligreatorhombated icositetrachoric tetracomb (great cellirhombated hexadecachoric tetracomb), stericantitruncated icositetrachoric tetracomb
cakix6Dcelliskewed hexeract1.581139
capicot4Dcelliprismated icositetrachoric tetracomb, great prismatotetracontaoctachoric tetracomb, steritruncated hexadecachoric tetracomb
capirsit4Dcelliprismatorhombisnubico tetracomb
capoht4Dcelliprismated demitesseractic tetracomb, tomoicositetrachoric-diprismatotesseractic tetracomb, steritruncated icositetrachoric tetracomb
capotat4Dcelliprismated tesseractic tetracomb, tomotesseractic-diprismatotesseractic tetracomb, steritruncated tesseractic tetracomb
cappin5Dcelliprismatedpenteract, steritruncatedpentacross2.423081
cappix (old: happix)5Dcelliprismatedhexateron, cellitruncated hexateron, hedratoprismated hexateron, steritruncated hexateron1.632993
cappixa (old: cappixalcappix)6Dcappix alterprism,cappix atop alternatecappix1.658312
caprohax6Dsmall celliprismatorhombatedhemihexeract, steriruncicantellated demihexeract, pentisteriruncichexeract3.278719
capshot4Dcelliprismatosnubhex tetracomb
capsthat4Dcelliprismatosnub truncatedhex tetracomb
capt5Dcelliprismatedtriacontiditeron, steritruncatedpenteract2.878460
captal6Dcelliprismatotruncatedheptapeton, steriruncitruncated heptapeton2.591194
captatit4Dcelliprismatotruncated tesseractic tetracomb, great tomocubic-diprismatotesseractic tetracomb, steriruncitruncated tesseractic tetracomb
capthix6Dsmall celliprismatotruncatedhemihexeract, steriruncitruncated demihexeract, pentistericantic hexeract3.278719
capticot4Dcelliprismatotruncated icositetrachoric tetracomb, celliprismatotruncated demitesseractic tetracomb, steriruncitruncated icositetrachoric tetracomb
captid (old: hiptid)5Dcelliprismatotruncateddodecateron, hedratoprismatotruncated dodecateron, steriruncitruncatedhexateron2.236068
captint5Dcelliprismatotruncatedpenteractitriacontiditeron, steriruncitruncatedpenteract, steriruncitruncatedpentacross3.701317
captog6Dcelliprismatotruncatedhexacontitetrapeton, steriruncitruncated hexacross4.123106
caquapin5Dcelliquasiprismatedpenteract1.276197
caquitpica3Dcubatiquasitrunciprismated cubatiapeiratic honeycomb
card (old: scard, shard)5D(small) cellirhombateddodecateron, small hedratorhombated dodecateron, stericantellatedhexateron1.658312
...4Dlonger antiduowedge,vertex figure ofcellirhombated dodecateron0.953463
cardip6Dcellirhombated-dodecateron prism1.732051
caricot (old: scaricot)4D(small) cellirhombated icositetrachoric tetracomb, great disicositetrachoric tetracomb, stericantellated icositetrachoric tetracomb
carnit (old: scarnit)5D(small) cellirhombatedpenteractitriacontiditeron, stericantellatedpenteract, stericantellatedpentacross2.660531
cartit (old: scartit)4D(small) cellirhombated tesseractic tetracomb, small rhombitesseractic-prismatotesseractic tetracomb, stericantellated tesseractic tetracomb
casch3Dcantic snub cubic honeycomb
catal6Dcellitruncatedheptapeton, steritruncated heptapeton1.851640
catax6Dcellitruncatedhexeract3.456841
cathix6Dcellitruncatedhemihexeract, steritruncated demihexeract, penticantichexeract2.598076
catjak (old: detidjik)6Dcellitruncatedicosiheptapeton (disteridisicosiheptaheptacontidipeton)2.581989
catog6Dcellitruncatedhexacontitetrapeton, steritruncated hexacross2.828427
cesratit4Doctahedra-alternated faceting ofscartit
cha2Dcomplexihexaapeirogonal tiling
chad5Dcellihemidodecateron1
...4Dvertex figure ofcellihemidodecateron0.866025
chado3Dchamfereddodecahedron,icosahedrally truncatedrhombic triacontahedron, Goldberg polyhedron GP(2,0)
chat (alt.: patex cube)3Dchamfered tetrahedron, partially tetrahedrally-expanded cube, tetrahedrally truncated cube, partially tri-expanded tetrahedron
chata2Dcomplexitrihexaapeirogonal tiling
chatit2Dcomplexitrihexagonal tiling
chexah3Dhyperboliccubic-hexagonal-tiling honeycomb, bitruncated order 4hexagonal-tiling honeycomb, bitruncated order 6cubic honeycomb1.870829i
chi4Dchirohecatonicosachoron, chiralcompound of 5ico1
chic3Dchamferedcube,octahedrally truncatedrhombic dodecahedron
chike3Dchamferedicosahedron,dodecahedrically truncatedrhombic triacontahedron
cho3Dcubohemioctahedron, rhomballelohedron1
...3Dcho+4{6/2} (?)1
choatut4Dcubohemioctahedron atoptruncated tetrahedron1.183216
choct3Dchamferedoctahedron,cubically truncatedrhombic dodecahedron
chon3Dcubic honeycomb, 3Dhypercubical honeycomb (δ3),Voronoi complex of primitive cubicallattice,Delone complex of primitive cubicallattice
...3Dcubically truncatedrhombic dodecahedral honeycomb
chont4Dhyperbolic (order 3)cubic-honeycomb tetracomb0.5i
chope4Dcubohemioctahedron prism1.118034
chopy, pt || cho4D(degenerate)cubohemioctahedron pyramid∞   i.e. flat in euclidean space
cid3Dsmall complex icosidodecahedron, (as type C:)complex polyhedronx2-3-o2-5-o20.951057
co   (alt.: ratet – old: ratit, rotet)3Dcuboctahedron, (small) rhombitetratetrahedron, rectifiedcube, rectifiedoctahedron, cantellatedtetrahedron, expanded tetrahedron, trigonal gyrobicupola,vertex figure ofoctet,lattice A3 contact polytope (span of its roots),lattice B3 contact polytope (span of its small roots), equatorial cross-section oftet-firstspid, equatorial cross-section ofoct-firstico1
...3D(ico derived)tridpy variant,o3m4o3o cell
...3D(tes derived)tridpy variant,o4m3o3o cell
...3D(hi derived)tridpy variant,o5m3o3o cell
...3Ddual ofpentagonal prism, (ex derived)pedpy variant,o3m3o5o cell
...4Daugmented axially-octahedral ursachoron ofxo3xooo4oooo&#xt...
coa tutcup, co || tutcup5Dco atoptuta1.224745
coaescu, co || escu, K-4.624Dcuboctahedron atopelongated square cupola1.447009
coaop, co || op, K-4.634Dcuboctahedron atopoctagonal-prism1.447009
coarit5Dco atoprit1.224745
coasirco, co || sirco, K-4.614Dcuboctahedron atopsmall rhombicuboctahedron1.447009
coasircope5Dcuboctahedron atopsmall-rhombicuboctahedron prism1.847759
coates5Dcuboctahedron atoptesseract1.050501
coatic, K-4.1294Dcuboctahedron atoptruncated cube,cuboctahedral cap ofsmall rhombated icositetrachoron2.613126
coaticbicu4Dcoatic bicupola
coatobcu4Dcoatoe bicupola, equatorially contractedrectified icositetrachoron
coatoe, co || toe, K-4.954Dcuboctahedron atoptruncated octahedron,cuboctahedral cap ofrectified icosatetrachoron1.732051
coatope (alt.: cotoe totric)5Dco atoptope, (co,toe,toe)-trigonic,co-first cap ofsibrant at (rico,rico)-margin2.236068
coatotum4Dbistraticco-cap ofprip,tut-diminishedprip,Stott expansion oftip, (co,toe)-based tutsachoron, (co,toe)-based tutism1.612452
coatut, co || tut, K-4.484Dcuboctahedron atoptruncated tetrahedron,cuboctahedral cap ofsmall rhombated pentachoron1.183216
coatuttip5Dco atoptuttip,co-first cap ofsarx1.290994
coatutu4Dexpanded axially-tetrahedral ursachoron, (co,tut)-based ursulate1.328131
cocube6Dcuboctahedron-cube duoprism1.322876
codibrox6Dtetracontaocta-diminishedbirectified hexeract1.414214
codify (alt.: hexgyi, trihexdip)8Dtetracontaocta-diminisheddischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton,hexadacachorongyro-icositetrachoronism,tegum sum of 3 pairwise bigyratedhexadecachoron duoprisms, tri-hexadecachoron-duoprism1
codip6Dcuboctahedron-cuboctahedron duoprism1.414214
codoe6Dcuboctahedron-dodecahedron duoprism1.721489
cogart (old: gocart)5Dcelligreatorhombatedtriacontiditeron, (great cellirhombated triacontiditeron), stericantitruncated pentacross3.534493
cograx (old: gocrax, goharx)5Dcelligreatorhombatedhexateron (great cellirhombated hexateron, great hedratorhombated hexateron), stericanitruncated hexateron2.327373
cograxa (old: cograxalcograx)6Dcograx alterprism,cograx atop alternatecograx2.345208
cogrin (old: gocrin)5Dcelligreatorhombatedpenteract (great cellirhombated penteract), stericantitruncated penteract3.988340
cohon3Dhyperbolic x4o3o4o3*a tesselation, cubic-octahedral honeycomb0.377964i
coid6Dcuboctahedron-icosidodecahedron duoprism1.902113
coike6Dcuboctahedron-icosahedron duoprism1.380039
cont4Dtetracontoctachoron, octagonny, bitruncatedicositetrachoron3.414214
..., cont || grico5D(degenerate)cont atopgrico∞   i.e. flat in euclidean space
contip5Dtetracontoctachoron prism, bitruncated-icositetrachoron prism3.450631
contit4Dtetracontoctachoric tetracomb,lamina-truncate of hyperbolico3x4x3o8o tesselation0.594604i
copal6Dcelliprismatedheptapeton, steriruncinated heptapeton1.963961
copatoe (alt.: coco totric)5Dcope atoptoe, (co,co,toe)-trigonic1.870829
copatope (old: copeatope)5Dcope atoptope,coatoe prism,cope-first monostratic cap ofricope1.802776
copatut5Dcope atoptut1.190238
cope, K-4.434Dcuboctahedron prism1.118034
copea tuttip5Dcope atoptuttip,cope-first monostratic cap ofsrippip1.284523
copen7Dcuboctahedron - pentachoron duoprism1.183216
cophix6Dsmall celliprismatedhemihexeract, steriruncinated demihexeract, pentisterichexeract2.179449
copog6Dcelliprismatedhexacontitetrapeton, steriruncinated hexacross3.316625
copox6Dcelliprismatedhexeract, steriruncinated hexeract3.087966
coprag6Dcelliprismatorhombatedhexacontitetrapeton, steriruncicantellated hexacross4.415880
copril6Dcelliprismatorhombatedheptapeton, steriruncicantellated heptapeton2.725541
coprix6D(small) celliprismatorhombatedhexeract, steriruncicantellated hexeract4.400450
copy, pt || co4D(degenerate)cuboctahedron pyramid∞   i.e. flat in euclidean space
coqroc4Dtetracontoctiquasirhombated tetracontoctachoron1.325654
corap7Dcuboctahedron - rectified-pentachoron duoprism1.264911
corit7Dcuboctahedron -rectified-tesseract duoprism1.581139
cosa2Dcomplexisquariapeirogonal tiling
cotco3Dcuboctatruncated cuboctahedron, cubitruncated cuboctahedron1.322876
cotcope4Dcuboctatruncated-cuboctahedron prism, cubitruncated-cuboctahedron prism1.414214
cotoe6Dcuboctahedron - truncated-octahedron duoprism1.870829
cotut totric5D(co,tut,toe)-trigonic1.732051
crag (old: scrag)6Dcellirhombatedhexacontitetrapeton, stericantellated hexacross3.082207
cral (old: scral)6Dcellirhombatedheptapeton, stericantellated heptapeton1.927248
crala7Dcellirhombated heptapeton alterprism,cellirhombated heptapeton atop invertedcellirhombated heptapeton1.936492
crax (old: scrax)6D(small) cellirhombatedhexeract, stericantellated hexeract3.277597
croc4Dtetracontoctirhombated tetracontoctachoron3.200413
crohax (old: scrohax)6D(small) cellirhombatedhemihexeract, pentiruncinated demihexeract, pentiruncichexeract2.397916
cuba octu5Dcube atop(oct,co)-ursachoron,(oct,co)-ursachoron based wedge1.994779
cuba sircope5Dcube atopsmall-rhombicuboctahedron-prism1.695040
cubaco, cube || co, K-4.354Dcube atopcuboctahedron,cubicalcupola1.031784
cubacope5Dcube atopcuboctahedron-prism1.120019
cubagike, cube || gike4Dcube atopgreat icosahedron1
cubaike, cube || ike, K-4.214Dcube atopicosahedron1
cubaope5Dcube atopoctahedral-prism0.895420
cubaquerco4Dcube atopquasirhombicuboctahedron,cubical cap ofquasidisprismatotesseractihexadecachoron0.890446
cubasc5D(degenerate)cubicalscalene, line atop fully orthogonalcube∞   i.e. flat in euclidean space
cubasirco, cube || sirco, K-4.714Dcube atopsmall rhombicuboctahedron,cubical cap ofsmall disprismatotesseractihexadecachoron1.485633
cubasquasc5Dcube atopsquasc1
cubatic, cube || tic4D(degenerate)cube atoptruncated cube∞   i.e. flat in euclidean space
cube (alt: squip)3Dcube, hexahedron, 3Dmeasure-polytope (γ3), geochor(id), squareprism, cantellated square dihedron, triangular antitegum, Voronoi cell of primitive cubicallattice, Delone cell of primitive cubicallattice, terminally chamferedtetrahedron, surtegmated tetrahedron0.866025
...4Dpyrithohedralcube-doe-bilbiro honeycomb
cubedoe6Dcube-dodecahedron duoprism1.647278
cubesirco6Dcube-small-rhombicuboctahedron duoprism1.645329
cubhex7Dcube-hexadecachoron duoprism1.118034
cubico7Dcube-icositetrachoron duoprism1.322876
cubid6Dcube-icosidodecahedron duoprism1.835220
cubike6Dcube-icosahedron duoprism1.286277
cubpen7Dcube-pentachoron duoprism1.072381
cubpy, K-4.264Dcubical pyramid, vertex-pyramid ofico1
cubpyp5Dcubpy prism1.118034
cuhsquah4Dcubihemisquare honeycomb, cell-alternatedcubical honeycomb
cute (old: cubdipy)4Dcubical (line-)tegum,cubicalbipyramid...
cutep5Dcubical-tegum prism, prism oftepepy...
cutpica3Dcubatitrunciprismated cubatiapeiratic honeycomb
cydadex4Dcyclical decadiminishing ofex1.618034
cydispan5Dcubically cyclodiminishedsmall-prismated-penteract1.914214
cyloh6Dcycloheptapetic hexacomb,Delone complex oflattice A6
cyooh7Dcyclo-octaexic heptacomb,Delone complex oflattice A7
cypit4Dcyclopentachoric tetracomb, pentachoric-dispentachoric tetracomb,Delone complex oflattice A4
cypropit5Dcycloprismatorhombated pentachoric tetrachomb, great prismatodispentachoric tetracomb, runcitruncated pentachoric tetrachomb
cytacoh3Dhyperbolic o3x4x3o4*a tesselation, cyclotruncated cubic-octahedral honeycomb0.944355i
cytatoh (old: batatoh)3Dcyclotruncated tetrahedral-octahedral honeycomb (butnot thehyperbolic cyclotruncated octahedral-tetrahedral honeycombcytoth), bitruncated tetrahedral-octahedral honeycomb, bitruncated alternated-cubic honeycomb, quarter cubic honeycomb
cytau tes4Dcyclotetraaugmentedtesseract, cyclotetradiminishedicositetrachoron1
cytaxh5Dcyclotruncated hexateric honeycomb
cyte cubau sodip4Dcyclotetracubaugmentedsodip...
cyte gysrit4Dcyclotetragyratedsmall rhombitesseract1.847759
cyte opau sodip4Dcyclotetraoctagon-prism-augmentedsodip...
cyted spic4Dcyclotetradiminishedsmall prismatotetracontoctachoron1.847759
cyted srit4Dcyclotetradiminishedsmall rhombitesseract, cyclotetraugmentedoctagonal duoprism1.847759
cytedbrag6Dcyclotetradiminishedbrag1.224745
cythdex4Dcyclical triangularily-hexagonally diminishedhexacosachoron1.618034
cyticth3Dhyperbolic x3o3o3x4*a tesselation, cyclotruncated cubic-tetrahedral honeycomb1.553774i
cytid rico4Dcyclotridiminishedrectified-icositetrachoron, metatridiminished rectified-icositetrachoron1.732051
cytid srico4Dcyclotridiminishedsmall rhombated icositetrachoron2.613126
cytitch3Dhyperbolic x3x3o3o4*a tesselation, cyclotruncated tetrahedral-cubic honeycomb1.391625i
cytloh6Dcyclotruncated heptapetic honeycomb
cytoch3Dhyperbolic x3x4o3o4*a tesselation, cyclotruncated octahedral-cubic honeycomb1i
cytopit4Dcyclotruncated pentachoric tetracomb, small truncated-pentachoric tetracomb
cytoth (old: cytitoh)3Dhyperbolic x3x3o4o3*a tesselation, cyclotruncated octahedral-tetrahedral honeycomb (butnot theeuclidean cyclotruncated tetrahedral-octahedral honeycombcytatoh)1.189207i
cyxh5Dcyclohexateric honeycomb,Delone complex oflattice A5

D

...3Dd3o3x, variation ofcuboctahedron2.661453
dacox5Ddodecacellihexateron1
dah5Ddishexadecateron,vertex figure ofkaje0.790569
dahi4Ddishecatonicosachoron3
dahiquatady4Ddishecatonicosiquasitruncated dishecatonicosachoron4.134026
dahitady4Ddishecatonicositruncated dishecatonicosachoron2.431014
daj (old: dije)6Ddisicosiheptapeton,vertex figure ofnal0.816497
damibdrox4Ddeep metabidiminishedrectified hexacosachoron3.077684
danbitot5Ddispenteractibitruncated triacontaditeron1.802776
danpit5Ddispenteractiprismated triacontaditeron2.5
dap, 10-ap3Ddecagonal antiprism1.674505
dapabdi poxic (alt.: hau sircope)4Ddeep parabidiminishedpoxic, hexa-augmentedsircope
dapabdi spic4Ddeep parabidiminishedsmall prismatotetracontoctachoron, hexa-gyro-augmentedtruncated-cube prism1.847759
dappip, K-4.964Ddecagonal-antiprism prism1.747560
dard tipady4Ddiretroditetrahedronary prismatodishecatonicosachoron1.414214
dasi3Ddisnub icosahedron,compound of 20oct (butnotaddasi)0.707107
daso (old: doso)3Ddisnub octahedron,compound of 8oct0.707107
dastop4Ddodeca-star toroidi-prism0.707107
...4Ddastop + 2 2did0.707107
datap4Dditetrahedronary prismatochoron,compound of 100hiddip1.414214
datcathi4Dditetrahedronary coincidic trishecatonicosachoron1.414214
dattady4Dditetrahedronary dishecatonicosachoron1.414214
dattathi4Dditetrahedronary trishecatonicosachoron1.414214
datteha3Dditetrahedronary tetrahemiapeiratic honeycomb
dawci, J903Ddisphenocingulum
day9Ddecayotton, 9Dsimplex (α9), pyroxenn(id),enneazettal pyramid,vertex figure ofux,Gosset polytope 080.670820
dazatrapeat2Dhyperbolic x∞x3o5*a tiling, diapeirogonal apeirogon-triangle-pentagon tiling, cyclotruncated apeirogon-triangle-pentagon tiling0.754758i
...4DDCBAVFfxoo xxxFofxFVo3xoxxFxooxo5ofxooxFfoV&#zx
deca4Ddecachoron, bitruncatedpentachoron, equatorial cross-section of (vertex first) q-pent, equatorial cross-section ofsrip-firstsibrid, equatorial cross-section ofpen-firstrin1.414214
deca agrip5Ddeca atopgrip,deca-first cap ofpirx1.914854
deca aprip5Ddeca atopprip1.620185
..., deca || gippid5D(degenerate)deca atopgippid∞   i.e. flat in euclidean space
decap5Ddecachoron prism1.5
dedip (old: dadip)4Ddecagon-decagon duoprism2.288246
dedjak6Ddecadiminishedicosiheptaheptacontidipeton0.816497
degpy, 10/3-pyr3Ddecagrammic pyramid0.636010
dehad5Ddodecahemidodecateron1
deker10Ddekeract, icosaxennon, 10Dmeasure-polytope (γ10), geodak(id)1.581139
depat2Dhyperbolic order 10 pentagonal tiling0.206652i
desided3Ddisnub icosidodecadodecahedron,compound of 2sided1.126898
detrat2Dhyperbolic order 10 triangular tiling0.393076i
dexdap4Ddodecahedral extended double antiprism1.618034
dibhid5Ddodecabiprismatohemidodecateron1
...4Dvertex figure ofdodecabiprismatohemidodecateron0.866025
did3Ddodecadodecahedron, great dodecadodecahedron1
...3Ddid+sidhei+gidhei (?)1
...4Ddid atop3doe (?)1.414214
dida raded, did || raded4Ddodecadodecahedron atoprhombidodecadodecahedron1.336349
didadoe4Ddid atopdoe1.414214
didamibdrox4Ddiminisheddeep metabidiminished rectified hexacosachoron3.077684
diddatigid, did || tigid4Ddodecadodecahedron atoptruncated great dodecahedron,did-first cap ofsirfix4.352502
diddip4Ddodecadodecahedron prism1.118034
diddoh3Dhyperbolic disdodecahedral honeycomb, hyperbolic bitruncated order 5 dodecahedral honeycomb1.798907i
didhi4Ddodecahedronary dishecatonicosachoron1
didpy, pt || did4D(degenerate)did pyramid∞   i.e. flat in euclidean space
digdom, ike-5-73Ddiminishedike-gad morpher, 5-fold pyramidal-symmetricike faceting with 5 trigs and 7 pigs
dih3Dhyperbolic bitruncated order 3 icosahedral honeycomb, hyperbolic disicosahedral honeycomb2.910693i
dihin (alt.: penalrap)5D(vertex-)diminishedhemipenteract,pentachoron atop alternaterectified pentachoron0.790569
dihinpy6Ddiminished-demipenteractic pyramid, (rap, dualpen, point)-trigonic0.816497
dihipap4Ddyad-hexagonal prismantiprismoid, s2s2s6x, edge-alternatedsitwadip...
dijak (alt.: taccahin)6D(mono-)diminished icosiheptaheptacontidipeton,tac atophin,vertex figure ofjaka0.816497
dijakpy7Ddiminished-icosiheptaheptacontidipetic pyramid, (hin,tac, point)-trigonic0.866025
...4Ddiminished 1/10-luna ofhexacosachoron1.618034
...4Dmono-diminished vertex-firstrotunda ofhexacosachoron1.618034
...4Ddiminishedthawro-wedged 1/6-luna ofhexacosachoron, {6},ike-wedge,ike,thawro,thawro-multiwedge...
dip (old: dep)3Ddecagonal prism1.693527
dippit4Ddisprismatotesseract1.485633
diquitdi4Ddisicositetraquasitruncated disicositetrachoron1.608038
dird3Ddirhimbidodecahedron,compound of 12pip0.986715
dirico4Ddiminishedrectified icosatetrachoron1.732051
dirid, J763Ddiminished rhombicosidodecahedron2.232951
dis3Ddisnubihedron,compound of 12tet0.612372
disco3Ddisnub cuboctahedron,compound of 2snic
disdi4Ddisnub disicositetrachoron1
disdi-verf3Dvertex figure ofdisnub disicositetrachoron0.866025
disdid3Ddisnub dodecadodecahedron,compound of 2siddid
dish3Dhyperbolic dissquare-tiling honeycomb, hyperbolic bitruncated order-4square tiling honeycomb1.553774i
dispap4Ddyad-square prismantiprismoid, s2s2s4x, edge-alternatedsodip...
dissid3Ddisnub icosidodecahedron,compound of 2snid
dissit3Ddisnub tetrahedron,compound of 4oct0.707107
distadedip4Ddecagon-decagram duoprism1.732051
disti4Ddisnub tetrakisicositetrachoron1.618034
ditatha2Dditrigonary trigonal hemiapeirogonal tesselation, alternate triangular tiling
ditdap4Ddigon-triangle duoantiprism, hemiatedshiddipsqrt[A2/2+B2]
ditdi4Ddisicositetratruncated disicositetrachoron2.326846
ditdia5Ddisicositetratruncated-disicositetrachoron alterprism2.352869
ditdid3Dditrigonal dodecadodecahedron,vertex figure ofdittady0.866025
...3Dditdid+gidtid (?)0.866025
ditdidap4Dditrigonary-dodecadodecahedron antiprism0.951057
ditdiddip4Dditrigonal-dodecadodecahedron prism1
ditdidpy4Dditdid pyramid, vertex pyramid ofdittady1
ditdih3Dhyperbolic ditrigonary disicosahedral honeycomb0.509376i
ditetaf (alt.: traltepe, penaltrip)5Ddiminishedtetaf, triangle atop gyratedtepe,pen atop gyratedtrip, (edge,perp triangle,gyrotrip)-trigonic0.790569
ditetetrat2Dhyperbolic order 4 tritetragonal tiling, hyperbolic ditetragonal tritetratrigonal tiling, hyperbolic alternated order 4 hexagonal tiling0.408248i
ditetpeat2Dditetratgonal triangle-pentagon-tiling, hyperbolic tripentagonal tiling of family o3o4o5*a0.357770i
ditetsquat (old: dittitecat)2Dhyperbolic order 3 tritetragonal tiling, hyperbolic ditrigonary triangle-square tiling, hyperbolic ditrigonary tritetragonal tiling, hyperbolic alternated octagonal tiling0.728238i
dithix4Dditrigonary hecatonicosihexacosichoron1.732051
ditoh3Dditetrahedral-octahedral honeycomb
ditoot2Dditrigonary octaoctagonal tiling, hyperbolic order 3 octagonal-octagrammic tiling0.557369i
ditra3Dditriangular trapezoprismsqrt[(a+b)2+c2]/2
ditrah3Dhyperbolic distriangular-tiling honeycomb2.075910i
dittadiu5Ddittady-based ursateron1.008123
dittadphi4Dditetrahedronary disprismatohecatonicosachoron1.414214
dittady4Dditrigonary dishecatonicosachoron1
...4Ddittady+dox (?)1
dittafady4Dditetrahedrofissary dishecatonicosachoron1.414214
dittec3Dditruncated cube, truncatedtruncated cube, expandedambified ticsqrt[(7+4 sqrt(2))y2+(24+16 sqrt(2))y+(24+16 sqrt(2))]/2
dittet3Dditruncated tetrahedron, truncatedtruncated tetrahedron, expandedambified tutsqrt[(11y2+36y+36)/8]
ditti3Dditrigonal icosahedron,vertex figure ofidhi1.401259
dittoe3Dditruncated octahedron, truncatedtruncated octahedron, expandedambified toesqrt[(5y2+9y sqrt(2)+9)/2]
ditusna4Ddisicosahedronary tetrasnubbachoron,compound of 20ex inrahi army,compound of 2kidisna1.618034
...4DWaterman polychoron number 5 wrt. alternated tessiclattice D4 centered at a hole2.121320
...3DWaterman polyhedron number 8 wrt. primitive cubiclattice C3 centered at a lattice point,Waterman polyhedron number 4 wrt. face-centered cubiclattice A3 centered at a deep hole2.121320
doa iddip5Ddodecahedron atopicosidodecahedron-prism1.738546
doa pabidrid, doe || pabidrid, K-4.1554Ddodecahedron atopparabidiminished rhombicosidodecahedron5.236068
doaid, doe || id, K-4.774Ddodecahedron atopicosidodecahedron,dodecahedral cupola1.618034
doasrid, doe || srid, K-4.1524Ddodecahedron atopsmall rhombicosidodecahedron,dodecahedral cap ofsmall disprismatohexacosihecatonicosachoron5.236068
doasridaid4Ddoe atopsrid atopid
doc4Ddistetracontoctachoron2.449490
dod honho4Ddisoctidishemioctintercepted hemioctachoron1
dodoe6Ddodecahedron-dodecahedron duoprism (or simply: dodecahedral duoprism)1.981679
doe3Ddodecahedron, cosmohedron, Goldberg polyhedron GP(1,0)1.401259
...4Drico-derived polychoron incorporatingdoes2.802517
..., doe || 6-dim-id || f-ike || doe4Daxially-pyritohedral (2,24,12,6)-diminishing ofex1.618034
..., doe || ipe5D(degenerate)doe atopipe∞   i.e. flat in euclidean space
doehon3Dhyperbolic order 4dodecahedral honeycomb0.899454i
doh honho4Ddisoctihemihexadekintercepted hemioctachoron1
...3DDohány synagoge polyhedron, Tabakgasse polyhedron1.080123
dohi7Ddodecahedron -hecatonicosachoron duoprism3.958754
dohitipady4Ddishecatonicositruncated prismatodishecatonicosachoron4.472136
dope, K-4.744Ddodecahedron prism1.487792
...4Dtoroidally parabideepeneddope, when drilled by twoikadoes...
dopix4Ddodecahedronary prismatohexacosachoron,compound of 60spid1
dot (alt.: rapa)5Ddodecateron, birectifiedhexateron, equatorial cross-section of (vertex first) 1/q-ax,rap alterprism,rap atop invertedrap,vertex figure ofmo,Gosset polytope 02,2, equatorial cross-section ofhix-firsthax0.866025
dotet6D(line,)dodecateron-tegum,dodecateron dipyramid
dotip6Ddodecateron prism1
dotpy6Ddodecateron pyramid, vertex pyramid ofmo1
dottascad6Ddodecateron atopsmall cellated dodecateron1
dottasibrid6Ddot atopsibrid,dot-first cap ofram1.732051
dottaspix6Ddodecateron atopsmall prismated hexateron,dot-first cap ofbirectified hexacontitetrapeton1.224745
dotu6Ddot-based ursapeton1.432173
dotum6Ddot-first bistratic cap oftim,dot-basedtutsatope,dot-based tutism2.645751
dox (old: gex)4Ddodecahedronary hexacosachoron (great hexacosachoron),compound of 25ico1
dri3Ddirhombicosahedron,compound of 20trip0.763763
dritit (old: sipstar)3Ddisrhombitritrihedron, "square-pentagon-pentagram(star)-thingy",vertex figure ofretroantiprismatosnub disicositetrachoron,edge facetingsidtid-3-0-6-3-b0.866025
dro3Ddirhombioctahedron,compound of 8trip0.763763
dudsi3Dsmall noble triangular hexecontahedron, dual of D-stellation oficosahedron, D-faceting ofdodecahedron,vertex figure ofpaphicki0.866025
duhd4Ddecahemidecachoron, copyropodichoron1
durat5Dcubic-tegmatic tetracontateron,rectified-triacontiditeron dual, joined penteract
dusidpith4Dsmall-prismated-tesseractihexadecachoron dual, triangular antitegmatic hexacontatetrachoron
duspid4Dsmall-prismated-decachoron dual, triangular antitegmatic icosachoron, crystalic icosachoron
dutip4Dtruncated-pentachoron dual, apiculated pentachoron, tetrakis pentachoron
...5Dpoint ||hex || gyrohex,Dutour polyteron type A
...7Dpoint || pseudohax ||gee,Dutour polyexon type A
...8Dpoint || pseudohesa ||zee,Dutour polyzetton type A
dygytpuf, K-4.134Ddyadic gyrotegmipucofastegium,3-prism atop reflected ortho3-prism0.866025

E

e3Dicosiicosahedron,compound of 10tet0.612372
ebauco3Delongatedbi-augmented cuboctahedron, 4fold elongated rhombohedron, bi-augmentedpexco...
ebdah hithi4Dexoblendic dishemihecatonicostrishecatonicosachoron2
ebot3Delongated bowtie tegum1
ebuthi4Dexotic blendic tetrishecatonicosachoron2
ecubedpy4Delongated cubical bipyramid, hexadiminishedicositetrachoron1
ecubpy4Delongated cubical pyramid, heptadiminishedicositetrachoron1
ecypit5Delongated cyclopentachoric tetracomb, elongated pentachoric-dispentachoric tetracomb
editetaf5Dedge-diminishedtetaf, (top base) edge-diminishing oftet-firstrotunda ofhin0.790569
editoh3Delongated ditetrahedral-octahedral honeycomb
efdit xithi4Dexofissary ditrigonal hexacositrishecatonicosachoron1.732051
eikedpy4Delongated icosahedral bipyramid
eikepy4Delongated icosahedral pyramid
ek8Ddiacosipentacontahexazetton,octacross (β8), aeroyott(id),octaexal antiprism,vertex figure ofvee, (one of the) Delone cell(s) oflattice E8,Gosset polytope 51,1,lattice C8 contact polytope (span of its small roots), equatorial cross-section of vertex-firstvee0.707107
ekip9Ddiacosipentacontahexazetton prism,vertex figure ofrake0.866025
endjak6Dennea-diminishedjak0.816497
ene8Denneazetton, 8Dsimplex (α8), pyroyott(id),octaexal pyramid,vertex figure ofday, (one of the) Delone cell(s) oflattice E8,Gosset polytope 070.666667
enep9Denneazetton prism,vertex figure ofru0.833333
enne9Denneract, octadecayotton, 9Dmeasure-polytope (γ9), geoxenn(id)1.5
eocta sirco4Delongatedoctasirco...
eoctaco4Delongatedoctaco
eoctatut4Delongatedoctatut
eoctpy4Delongatedoctahedral pyramid, diminishedpex hex
epcu, J203Delongated pentagonal cupola
epedpy, J163Delongated pentagonal dipyramid
epeppy, J93Delongated pentagonal pyramid
epgybro, J433Delongated pentagonal gyrobirotunda
epgycuro, J413Delongated pentagonal gyrocupolarotunda
epigybcu, J393Delongated pentagonal gyrobicupola
epipdapy4Delongatedpentagonal-prismatic bipyramid...
epippy4Delongatedpentagonal-prismatic pyramid...
epobcu, J383Delongated pentagonal orthobicupola
epobro, J423Delongated pentagonal orthobirotunda
epocuro, J403Delongated pentagonal orthocupolarotunda
epro, J213Delongated pentagonal rotunda
erad3Dexpandedrhombic dodecahedron
erhote3Dexpandedrhombic triacontahedron
erich3Dparallellythat elongatedrich
esch3Dedge-snub cubic honeycomb
escu, J193Delongated square cupola, diminished small rhombicuboctahedron1.398966
escupe, K-4.684Delongated-square-cupola prism1.485633
esircoatic4Delongatedsircoatic, diminishedsrit
esquidpy, J153Delongated square dipyramid
esquidpyp4Delongated square dipyramid prism, J15 prism...
esquigybcu, J37 (alt.: pirco)3Delongated square gyrobicupola, pseudorhombicuboctahedron, Miller's solid1.398966
esquippidpy4Delongated square-pyramidal bipyramid,esquidpy-wedge, half of partially (mono-)expandedhex
esquipuf4Delongatedsquare pucofastegium, square atopoctagon-prism atopoctagon-prism
esquipy, J83Delongated square pyramid
esquipyp4Delongatedsquare-pyramidal-prism,elongated-square-pyramid prism, externalblend ofsquare-pyramidal prism andtesseract
etcu, J183Delongated triangular cupola
etedpy4Delongated tetrahedral bipyramid
etepe4Delongatedtetrahedral-prism,elongated-triangular-pyramid prism, externalblend oftetrahedral prism and(triangle,square)-duoprism
etepy4Delongated tetrahedral pyramid
etetaco4Delongatedtetaco...
etidpy, J143Delongated trigonal dipyramid
etigybcu, J363Delongated triangular gyrobicupola
etobcu, J353Delongated triangular orthobicupola
etoh3Delongatedtetrahedral-octahedral honeycomb, elongatedalternated cubic honeycomb
etoph3Delongated-triagonal prismatic honeycomb
etrat2Delongated triangular tiling
...3Dblend ofelongated triangular-tiling prisms
etripdapy4Delongatedtrigonal-prismatic bipyramid...
etrippy4Delongatedtrigonal-prismatic pyramid...
etripuf4Delongatedtrigonal pucofastegium...
etripy, J73Delongated triangular pyramid
etutatoe4Delongatedtutatoe...
...4Dex+fix (?)1.618034
...4Dex+gohi+120id (?)1.618034
ex, pT4Dhexacosachoron, 600-cell, hydrochoron, tetraplex, polytetrahedron1.618034
...3Dexpanded dodeca-augmented great rhombicuboctahedron...
exip5Dhexacosachoron prism1.693527
...3Dexternalblend of asidtid and 12stiscu
extoh3Dexpandedoctahedral-tetrahedral honeycomb
exu5D(degenerate)ex-based ursateron∞   i.e. flat in euclidean space

F

...3Df v10o, variation ofdecagonal prism, hull of10/3-prism1.286277
...3Df v3o, variation oftriangular prism,vertex figure ofrectified great grand hecatonicosachoron0.884212
...3Df v5o, variation ofpentagonal prism,vertex figure ofrighi0.964832
...3Df x3o, variation oftriangular prism,vertex figure ofrectified hecatonicosachoron0.993902
...4Df x3o3o, variation oftetrahedron prism,vertex figure ofrectified hyperbolic hecatonicosachoric honeycomb1.014647
...3Df x4o, variation ofcube1.074481
...3Df x5/2o, variation of5/2-prism,vertex figure ofraghi0.964832
...3Df x5o, variation ofpentagonal prism1.173932
...3Df3o3x, variation ofcuboctahedron1.327129
...3Df3o4x, variation ofsmall rhombicuboctahedron1.789732
...3Df3o5x, variation ofsrid, hull ofsiid, hull ofquit gissid2.785428
...3Df3v5v, variation ofgrid, hull ofidtid3.236068
...3Df3x5o, variation ofti, hull oftigid, hull ofgaddid3.036797
...3Df3x5x, variation ofgreat rhombicosidodecahedron, hull ofquitdid4.341518
fatfipte4Dfaceted terifacetedhyperbolic order 5 pentachoric honeycomb0.393076i
fawdint5Dfrustisphenary dispenteractitriacontaditeron, fastegiverted dispenteractitriacontaditeron0.914214
...4DFAxoAFxoxx3FxAAoxFxox oxofofxFof3ooxofxfoFf&#zx
...4DFAxoFFxoox3foFFxofoxo oxofofxFof3ooxofxfoFf&#zx
...4DFAxoFFxxo3foFFxofxx oxofofxFo3ooxofxfoF&#zx
...4DFAxoFFxxox3foFFxofxxo oxofofxFof3ooxofxfoFf&#zx
...4DFAxoFFxxox3foFFxofxxo xoxFxFoAxF3oxxofxFoFf&#zx
fe6Dtetradecapeton, tritruncatedheptapeton, equatorial cross-section of (vertex first) q-hept1.732051
fedandoh5Dfacetodispenteractidishexadecateron1.274755
fenandoh5Dfacetospinopenteractidishexadecateron1.274755
...4Dvertex figure offacetospinopenteractidishexadecateron0.919866
...4DFfxo oxFx3xfox5xoxx&#zx
...4DFfxo xofo3ofox5xoxx&#zx
fib8Ddischiliahectohexaconta-diacositetraconta-zetton1
fidoh5Dfacetoinverted decahexadecateron1.274755
...4Dvertex figure offacetoinverted decahexadecateron0.919866
fighitte4Dfaceted great hecatonicosachoric tetracomb0.393076i
fipech3Dhyperbolic o5/2o5o4x honeycomb, hyperbolic faceted order-5 cubic honeycomb0.555893i
fipped3Dfacetedhyperbolic order 5 dodecahedral honeycomb0.427486i
fipte4Dhyperbolic pentagrammic-order hexacontachoric tetracomb, faceted hyperbolic pentachoric tetracomb0.393076i
firgaghi4Dfaceted rectified great grand hecatonicosachoron1.070466
firgogishi4Dfacetorectified great grand stellated hecatonicosachoron0.661585
firl6Dfacetorectified heptapeton0.845154
firn5Dfacetorectified penteract1.414214
firp4Dfaceted rectified pentachoron, retropyrohemiperichoron,vertex figure ofdah, tetrahedralcuploid0.774597
...4Dfirp+rap+15{4} (?)0.774597
firsashi4Dfaceted rectified small stellated hecatonicosachoron2.802517
firt4Dfacetorectified tesseract1.224745
firx5Dfacetorectified hexateron0.816497
fitetaltet4Dfacetedtet atop dual3tet,vertex figure ofphap0.707107
fitetaoct4Dfaceted3tet atopoct0.774597
...4Dfix+gahi+120id (?)1.618034
fix, pI4Dicosahedral hecatonicosachoron, facetedhexacosichoron, polyicosahedron1.618034
..., fix || padohi5D(degenerate)fix atoppadohi∞   i.e. flat in euclidean space
...3Dβ2β5o, (mere) alternatedpip0.986715
fohaf6Dtetradecahemitetradecapeton1
...4Dfooo3xxoF3xfxo *b3oxFo&#zx
...4Dtriacontapenta-diminishedhexacosachoron, fooo5ofxo xofx5oxox&#zx1.618034
forx6Dfacetorectified hexeract1.581139
frasa7Dfacetorectified hepteract1.732051
frico4Dfacetorectified icositetrachoron1.732051
fro8Dfacetorectified octeract1.870829
froc7Dfacetorectified octaexon0.866025
frogfix4Dfaceted rectified great faceted hexacosichoron0.726543
froghi4Dfacetorectified great hecatonicosachoron1.902113
frogshi4Dfacetorectified great stellated hecatonicosachoron1.175571
frox4Dfaceted rectified hexacosichoron3.077684
...4Dfrox+600 2thah (?)3.077684
fry4Dfacetorectified hecatonicosachoron4.534568
...4DFxFox5xFoFx xofox5oxofx&#zx
...4Ddodeca-diminished equatorial tetrastratic segment ofrox3.077684
...4DFxo oxf3xox5xfo&zxt
...4Dequatorial tetrastratic segment ofrectified hexacosachoron3.077684
...4DFxox3xoxf3oFxx *b3oxfo&#zx
...4DFxxox5ofxfo xofox5oxofx&#zx
...4DFxxx3xxoF3xfxo *b3oxFo&#zx
...4DFxxx5ofxo xofx5oxox&#zx
fy8Ddischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, siderozetton,Gosset polyzetton 41,2, Witting polytope,vertex figure ofgoh,lattice E8 contact polytope (span of its roots)1

G

gabach7Dgreat bicellihexadecaexon3.872983
gabbadipady4Dgreat blendic disprismatodishecatonicosachoron2
gabbathi4Dgreat blendic trishecatonicosachoron2
gabdacan5Dgreat biprismatodiscellipenteract1.021221
...4Dvertex figure ofgreat biprismatodiscellipenteract1.118034
gabippady (old: gabbippady)4Dgreat blendic prismatodishecatonicosachoron2
gabirch3Dgreat birhombatocubic honeycomb
gaborg6Dgreat birhombihexacontitetrapeton, bicantitruncated hexacross3.391165
gaborx6Dgreat birhombatedhexeract, bicantitruncated hexeract4
gabred4Dgreat birhombatodecachoronsqrt[(2a2+2ab+3b2)/5]
gabreth3Dgreat birhombitetrahedral honeycomb
gabric4Dgreat birhombatotetracontoctachoronsqrt[a2 + 2 sqrt(2) ab + 3b2]
gabril6Dgreat birhombatedheptapeton, bicantitruncated heptapeton2.390457
gabrim (old: prarm, older: girmak, oldest: gokorm)6Dgreat birhombated pentacontitetrapeton (prismatorhombated rectified pentacontitetrapeton), bicantitruncated pentacontitetrapeton5.385165
gacal6Dgreat cellatedheptapeton, steriruncicantitruncated heptapeton3.380617
gacdincat5Dgreat cellidispenteracticellitriacontaditeron1.683979
gacdupthix4Dsmall capped dipentary tetrishecatonicosahexacosichoron1.328131
gacicot (old: otit)4Dgreat cellated icositetrachoric tetracomb, omnitruncated icositetrachoric tetracomb
gacid3Dgreat complex icosidodecahedron0.587785
gacnet5Dgreat cellatedpenteractitriacontiditeron, omnitruncatedpenteract, omnitruncatedpentacross4.829189
gacnetip6Dgreat-cellated-penteractitriacontiditeron prism4.855004
gacoca3Dgreat cubaticubatiapeiratic honeycomb
gacocaddit3Dhyperbolic x3o3o4o3*a tesselation, grand cuboctahedronary cubic-distetrahedral honeycomb0.511081i
gacotat (old: otatit)4Dgreat cellated tesseractic tetracomb, omnitruncated tesseractic tetracomb
gacquitpica3Dgreat cubatiquasitrunciprismated cubatiapeiratic honeycomb
gactanet5Dgreat cellitrispenteractitriacontaditeron1.683979
gactipeca3Dgreat cubatitrunciprismated cubatiapeiratic honeycomb
gad3Dgreatdodecahedron, faceted icosahedron,vertex figure offix0.951057
gad phiddix4Dgreat dipentary hecatonicosadishexacosachoron1.328131
gadadoe4Dgreat dodecahedron atopdodecahedron1.618034
gadatady4Dgrand ditetrahedral dishecatonicosachoron0.874032
gadathiphi4Dgrand ditetrahedronary hecatonicosaprismatohecatonicosachoron0.874032
...4Dgadathiphi+600 2tet (?)0.874032
gaddadid, gad || did4Dgreat dodecahedron atopdodecadodecahedron,great-dodecahedralcupola1.064815
gaddaraded, gad || raded4Dgreat dodecahedron atoprhombidodecadodecahedron,gad-first cap ofquipdohi1.328131
gaddatigid, gad || tigid4D(degenerate)gad atoptigid∞   i.e. flat in euclidean space
gaddid3Dgreat dodekicosidodecahedron0.716891
gaddiddip4Dgreat-dodekicosidodecahedron prism0.874032
gaddip4Dgreat-dodecahedron prism1.074481
gaddit thix4Dgrand ditrigonal trishecatonicosihexacosachoron1.732051
gadencorn5Dgreat dispinocellirhombated penteract1.192297
...4Dvertex figure ofgreat dispinocellirhombated penteract0.907821
gadinnert5Dgreat dispenteractirhombated triacontaditeron2.336045
gadixady4Dgreat dishexacosadishecatonicosachoron3.139124
gadixhix (old: gixhix)4Dgreat dodecahedronary hexacosahemihexacosachoron,compound of 25ihi (butnotsadixhix)1
gadpy4Dgreat-dodecahedral pyramid, vertex cap offix1.618034
gadsadox4Dgreat disnub dihexacosachoron0.726543
gadsid3Dgreat disnub dodecahedron,compound of 12pap0.951057
gadtacaxady4Dgreat ditetrahedronary cubihexacosidishecatonicosachoron0.874032
gadtachi4Dgrand ditetrahedronary cubihecatonicosachoron0.874032
gadtap4Dgreat ditetrahedronary prismatochoron,compound of 36stadidip0.874032
gadtatdic3Dhyperbolic grand ditetrahedronary tetrahedral-discubic honeycomb0.722778i
gadtaxadiap5Dgrand ditetrahedronary hexacosadishecatonicosachoron atop alternategrand ditetrahedronary hexacosadishecatonicosachoron,grand ditetrahedronary hexacosadishecatonicosachoron alterprism0.951057
gadtaxady4Dgrand ditetrahedronary hexacosadishecatonicosachoron0.874032
gadtaxhi4Dgreat ditetrahedronary hexacosihecatonicosachoron0.874032
gadtaxhiap5Dgrand ditetrahedrary hexacontahecatonicosachoron antiprism0.951057
gadtef pixady4Dgreat ditetrahedronary exofissary prismatohexacosadishecatonicosachoron0.874032
gadtifady (old: gadtafady)4Dgreat ditetrahedronarofissary dishecatonicosachoron0.874032
gaedit pathi4Dgrand exoditetrahedronary prismatotriakishecatonicosachoron0.874032
gafthi4Dgreat antifrustary trishecatonicosachoron2.236068
...3Dvertex figure ofgreat antifrustary trishecatonicosachoron0.816497
gafwan5Dgreat facetosphenary penteract0.792893
...4Dvertex figure ofgreat facetosphenary penteract0.776106
...4Dgaghi+didhi (?)1
...4Dgaghi+idhi (?)1
...4Dgaghi+paphacki+sridaphi (?)1
...4Dgaghi+sridixhi (?)1
gaghi, gapD4Dgreat grandhecatonicosachoron, greatened aggrandized polydodecahedron1
..., gaghi || gofix5D(degenerate)gaghi atopgofix, (degenerate)gaghi antiprism, (degenerate)gofix antiprism∞   i.e. flat in euclidean space
gaghipy, pt || gaghi5D(degenerate)gaghi pyramid∞   i.e. flat in euclidean space
gahax7Dgee atophax,gee-first segment ofnaq0.866025
gahfipto4Dgreat hexadecafeceted prismatotesseractioctachoron0.890446
...4Dgahi+gohi (?)1.618034
gahi, apD4Dgrandhecatonicosachoron, aggrandized polydodecahedron1.618034
gaid tathi4Dgrand inverted ditetrahedronary trishecatonicosachoron0.874032
gaje (old: gaj, older: gij)6Dgreat icosiheptaheptacontidipeton0.816497
gakevatant5Dgreat skewverted trispenteractitriacontaditeron1.429298
gakvebidant (old: gikkivbadant)5Dgreat skewverted biprismatodispenteractitriacontaditeron1.429298
ganbathi4Dgreat spinoblendic trishecatonicosachoron2
ganbippady4Dgreat spinoblendic prismatodishecatonicosachoron2
gancpan5Dgreat spinocelliprismated penteract1.276197
...4Dvertex figure ofgreat spinocelliprismated penteract0.920055
gap4Dgreat antiprism, grand antiprism, pentagonal double antiprismoid (butnot:great duoantiprism), bicyclical decadiminishing ofex1.618034
...4Dpentagonal double antitegmoid, pentaantitegmatoswirlic hectochoron, dual ofgreat antiprism...
...3Dcell ofgap dual, adjacent bikisdoe
gapcyxh5Dgreat prismated cyclohexateric honeycomb,Voronoi complex oflattice A5*
gapil6Dgreat prismatedheptapeton, runcicantitruncated heptapeton2.803060
gappip5Dgreat-antiprism prism1.693527
gapquinoh5Dgreat prismated quarterpenteractic pentacomb
gapript4Dgreat pseudorhombated prismatotesseract0.765367
...4Dgapript+16 2thah (?)0.765367
gapthi4Dgrand prismatotriakishecatonicosachoron2.400819
gaqri4Dgreat quasirhombated icositetrachoron1.230739
gaqrich3Dgreat quasirhombated cubic honeycomb
gaqrigafix4Dgreat quasirhombated great faceted hexacosachoron1.080363
gaqrigaghi4Dgreat quasirhombated great grand hecatonicosachoron1.679184
gaqrigagishi4Dgreat quasirhombated great grand stellated hecatonicosachoron1.179024
gaqrigashi4Dgreat quasirhombated great stellated hecatonicosachoron2.700333
gaqrigohi4Dgreat quasirhombated great hecatonicosachoron2
gaqrin5Dgreat quasirhombated penteract1.673396
gaqript4Dgrand quasirhombated prismatotesseract0.765367
gaqrisashi4Dgreat quasirhombated small stellated hecatonicosachoron5.018002
gaqrit4Dgreat quasirhombated tesseract1.401594
gaqrox6Dgreat quasirhombihexeract1.906840
gaquacint5Dgreat quasicellated penteractitriacontiditeron3.029675
gaquacox6Dgreat quasicellatedhexeract3.821061
gaquapac4Dgreat quasiprismatotetracontoctachoron1.127864
gaquapan5Dgreat quasiprismated penteract2.527061
gaquapech3Dgreat quasiprismated cubic honeycomb
gaquatid3Dgreat quasitruncated icosidodecahedron, stellatruncated icosidodecahedron1.020684
gaquatiddip4Dgreat-quasitruncated-icosidodecahedron prism1.136572
gaquidapixhi4Dgreat quasidisprismatohexacosihecatonicosachoron1.581630
gaquidipdy4Dgrand quasidisprismatodishecatonicosachoron1.695697
gaquidphihi4Dgreat quasidisprismatohecatonicosihecatonicosachoron4.242641
gaquidpoth4Dgreat quasidisprismatotesseractihexadecachoron1.938391
gaquidpothip5Dgreat-quasidisprismatotesseractihexadecachoric prism, great-quasiprismated-tesseract prism2.001839
gaquipadah4Dgreat quasiprismatodishexadecachoron0.890446
gaquitxog6Dgreat quasiterated hexeractihexacontatetrapeton4.288753
garag7Dgee atoprag,gee-firstrotunda ofrez1
garawv hixhi4Dgreat retrosphenoverted hecatonicosihexacosihecatonicosachoron1.054256
garcornit5Dgreat retrocellirhombated penteractitriacontaditeron1.192297
gard tadhix4Dgrand retroditetrahedronary dishecatonicosihexacosachoron0.874032
gardatady4Dgrand retroditetrahedral dishecatonicosachoron0.874032
...4Dgardatady+1440{5}0.874032
gardatathi4Dgrand retroditetrahedronary trishecatonicosachoron0.874032
gardtapaxhi4Dgrand retroditetrahedronary hexacosidishecatonicosachoron0.874032
gardtaxady4Dgrand retroditetrahedronary hexacosidishecatonicosachoron0.874032
gari3Dgreat antirhombicosahedron,compound of 5cho1
garpit4Dgrand rhombated dishexadecachoron1.847759
garpop4Dgrand rhombated prismatopentachoron1.183216
gart5Dgreat rhombatedtriacontiditeron, cantitruncated pentacross2.645751
garx5Dgreat rhombatedhexateron, cantitruncated hexateron2
gashi, aspD4Dgrand stellatedhecatonicosachoron, aggrandized stellated polydodecahedron0.618034
gashia5Dgrand stellated hecatonicosachoron antiprism,grand stellated hecatonicosachoron alterprism,grand stellated hecatonicosachoron atop dualgrand stellated hecatonicosachoron0.707107
gassic3D(chiral) great snub cube,compound of 3squap0.822664
gassid3Dgreat snub dodecahedron,compound of 6pap0.951057
gatopin5Dgreat pteroprismated penteract0.914214
...4Dvertex figure ofgreat pteroprismated penteract0.837186
...4Dgax+gashi+120gid (?)0.618034
...4Dgax+gofix (?)0.618034
gax, apT4Dgrandhexacosachoron, aggrandized polytetrahedron0.618034
gaxu5Dgax-based ursateron1.008123
gedak6Dhexacontitetradishexeract,compound of 2hax0.866025
gee (old: xic)6Dhexacontitetrapeton,hexacross (β6), aeroex(id),hexateral antiprism,triacontaditeric bipyramid,octahedral duotegum, square triotegum,vertex figure ofzee,Gosset polytope 31,1,lattice C6 contact polytope (span of its small roots), equatorial cross-section of vertex-firstzee0.707107
geeasc8Dhexacontitetrapetonscalene, half ofhecatonicosoctaexon pyramid, quarter ofdiacosipentacontahexazetton0.707107
geedatepthi4Dgreat exoditetrahedrary prismatotrishecatonicosachoron1.414214
geep7Dhexacontitetrapeton prism, hexacross prism,vertex figure ofrek0.866025
geepy7Dhexacontitetrapeton pyramid, vertex-firstrotunda ofgee0.707107
gefdit dixdy4Dgreat exofissary ditrigonal dihexacosadihecatonicosachoron1.732051
gefidtethi4Dgreat exofissary ditetrahedronary tetrakishecatonicosachoron0.874032
gefirdit xethi4Dgreat exofissary retroditetrahedronary hexacositrishecatonicosachoron1.414214
gefradit thix4Dgreat exofissary retroditetrahedronary triakishecatonicosihexacosachoron0.874032
gefridit xethi4Dgreat exofissary retroinverted ditetrahedronary hexacositrishecatonicosachoron1.414214
geihid3Dgreat icosihemidodecahedron0.618034
geihiddip4Dgreat-icosihemidodecahedron prism0.794963
gektabcadont (old: giktabacadint)5Dgreat skewtrigonary biprismatocellidispenteractitriacontiditeron1.5
getatixady4Dgreat tritrigonary hexacosidishecatonicosachoron1.136572
getdoca (old: gotactictosquath)3Dgreat tetradicubatiapeiratic honeycomb, great tetrahedral cubic tomocubic tomosquare tiling honeycomb
getit cadoca3Dgreat tritrigonary cubatidicubatiapeiratic honeycomb
getit dixady4Dgreat tritrigonal dihexacosidihecatonicosachoron1.136572
getit phiddix4Dgreat tritrigonal prismatohecatonicosidishexacosachoron1.136572
getit pixady4Dgreat tritrigonal prismatohexacosidihecatonicosachoron1.136572
getit thix4Dgreat tritrigonal trishecatonicosihexacosachoron1.136572
getit xethi4Dgreat tritrigonal hexacositrishecatonicosachoron1.136572
getitdin5Dgreat tesseractitriacontidiadispenteract1.276197
getut4Dgreat tristetracosioctacontachoron1
...3Dvertex figure ofgetut0.866025
ghaha2Dgreat hexahexaapeirogonal tiling
ghahoh4Dgreat hexadecahemihexadecachoron1
gheat2Dgreat heptagonal tiling, hyperbolic order 7/2 heptagon tiling0.873057i
ghihi4Dgreat hecatonicosihecatonicosachoron0.854102
ghipady4Dgreat hecatonicosiprismatodishecatonicosachoron4.087567
ghothat, (inbetween: ghath)2Dgreat hexagonal-trigonal-hexagonal tiling
gibacadint5Dgreat biprismatocellidispenteractitriacontaditeron1.683979
gibcotdin5Dgreat biprismatocellitriacontadiadispenteract2.001839
gibil biro3Dgreat bilunabirotunda
gibpof6Dgreat biprismated tetradecapeton, biruncicantitruncated heptapeton3
gibrant5Dgreat birhombated penteractitriacontiditeron, bicantitruncated penteract3.391165
gibricot4Dgreat birhombated icositetrachoric tetracomb, great grand prismatodisicositetrachoric tetracomb
gibrid (old: gadrid)5Dgreat birhombateddodecateron, bicantitruncatedhexateron2.179449
gibtadin5Dgreat biprismatotriacontadiadispenteract1.488108
gic4Dgreat tetracontoctachoron, octagrammy0.585786
gicalico5Dgreat icositetrachoron atop dualicositetrachoron,blend of 3icateses1.050501
gicdatrid3Dgreat complex (ditrigonary) rhombicosidodecahedron0.866025
gichado4Dgreat cubihexadecadisoctachoron1.174172
gico4Dgreat icositetrachoron, stella prismata,compound of 3tes1
...4Dgico+8co+16 2thah (?)1
gid3Dgreat icosidodecahedron0.618034
gid thipady4Dgreat ditrigonary hecatonicosiprismatodishecatonicosachoron4.087567
gid tipathi4Dgreat ditrigonal prismatotriakishecatonicosachoron2.920251
...3Dgid+geihid+gidhid (?)0.618034
gidacadint5Dgreat discellidispenteractitriacontaditeron1.683979
gidard tipady4Dgreat diretroditetrahedronary prismatodishecatonicosachoron1.414214
gidasid3Dgreat invertidisnub dodecahedron,compound of 12starp0.587785
giddasid3Dgreat disnub icosidodecahedron,compound of 2gosid
giddatady4Dgreat ditetrahedronary dishecatonicosachoron1.414214
giddic4Dgreat distetracontoctachoron0.765367
giddip4Dgreat-icosidodecahedron prism0.794963
giddird3Dgreat dirhombidodecahedron,compound of 12stip0.725530
giddit thix4Dgreat ditrigonal trishecatonicosihexacosachoron1.732051
gidditdid3Dgreat ditrigonary dodekicosidodecahedron, great dodekified icosidodecahedron1.134229
gidditdid aidtid4Dgreat ditrigonary dodekicosidodecahedron atopicosidodecatruncated icosidodecahedron4.684471
gidditdiddip4Dgreat-ditrigonary-dodekicosidodecahedron prism1.239546
gidditdy4Dgreat ditrigonary dishecatonicosachoron1.732051
gidditpix4Dgreat ditrigonary prismatohexacosichoron1.732051
giddy3Dgreat dodekicosahedron1.134229
...3Dgiddy+12{10/2} (?)1.134229
...3Dgiddy+20{6/2}1.134229
gidhei3Dgreat dodecahemicosahedron, small dodecahemiicosahedron (butnotsidhei)1
gidhid3Dgreat dodecahemidodecahedron0.618034
gidhiddip4Dgreat-dodecahemidodecahedron prism0.794963
gidhiquit paddy4Dgreat dishecatonicosaquasitruncated prismatodishecatonicosachoron2.140933
gidipthi4Dgreat dipental trishecatonicosachoron1.328131
gidisdrid3Dgreat disnub dirhombicosidodecahedron, Skilling's spectre0.707107
gidpicdoh3Dhyperbolic great disprismated cubical-dodecahedral honeycomb, hyperbolic omnitruncated order 5 cubical honeycomb, hyperbolic omnitruncated order 4 dodecahedral honeycomb4.248159i
gidpith4Dgreat disprismatotesseractihexadecachoron, great prismatedtesseract, omnitruncated tesseract3.498949
gidpithip5Dgreat-disprismatotesseractihexadecachoric prism, great-prismated-tesseract prism, central segment ofcogart3.534493
gidpixathi4Dgreat dipentagonal hexacositrihecatonicosachoron1.328131
gidpixhi4Dgreat disprismatohexacosihecatonicosachoron, omnitruncatedhecatonicosachoron, omnitruncatedhexacosachoron12.786651
gidpixhip5Dgreat-disprismatohexacosihecatonicosachoron prism, omnitruncated-hexacosachoron prism12.796423
gidrid (subsym.: gidrikid)3Dgreat dirhombicosidodecahedron, great snub disicosidisdodecahedron, Miller's monster, (subsym.: great dirhombichiricosadodecahedron)0.707107
gidriddip4Dgreat-dirhombicosidodecahedron prism, great-snub-disicosidisdodecahedron prism, prism of Miller's monster0.866025
gidrissid3Dgreat diretrosnub icosidodecahedron,compound of 2girsid
gidsac3Dgreat disnub cube,compound of 6squap0.822664
gidsid3Dgreat invertidisnub icosidodecahedron,compound of 2gisid
gidthidy hi4Dgreat ditrigonal hecatonicosadishecatonicosihecatonicosachoron1.732051
gidthixhi4Dgreat ditrigonary hecatonicosihexacosihecatonicosachoron3.139124
gidtid3Dgreat ditrigonary icosidodecahedron,vertex figure ofgidtixhi0.866025
gidtidagiid4Dgreat ditrigonary icosidodecahedron atopgreat icosicosidodecahedron,gidtid cap ofgetit phiddix1.136572
gidtidap4Dgreat-ditrigonary-icosidodecahedron antiprism0.951057
gidtiddip4Dgreat-ditrigonary-icosidodecahedron prism1
gidtidpy4Dgidtid pyramid, vertex pyramid ofgidtixhi1
gidtixhi4Dgreat ditrigonary hexacosihecatonicosachoron1
...4Dgidtixhi+dox (?)1
gidtixhipy, pt || gidtixhi5D(degenerate)gidtixhi pyramid∞   i.e. flat in euclidean space
gidtixhiu5Dgidtixhi-based ursateron1.008123
gifdahihox4Dgreat fissary dodecahedronary hecatonicosihemihexacosachoron1
gifodib3Dsidtidfaceting sidtid-2-10-20-0 (i.e. with 10(=d) {3}, 20(=i) {4}, and 2(=b) {5/2})0.866025
giid3Dgreat icosicosidodecahedron1.134229
giidip4Dgreat-icosicosidodecahedron prism1.239546
gik vadixady4Dgreat skewverted dishexacosidishecatonicosachoron2.013884
gik vipathi4Dgreat skewverted prismatotriakishecatonicosachoron2.828427
gik vixathi4Dgreat skewverted hexacositriakishecatonicosachoro2.013884
gikagid, gike || gid4Dgreat icosahedron atopgreat icosidodecahedron,great icosahedral cap ofrectified grand hexacosachoron,great-icosahedralcupola0.726543
gikaike4Dgreat icosahedron atopicosahedron1
gike3Dgreaticosahedron, retrosnubtetrahedron, retrosnub tetratetrahedron, edgifiedpenta-stellahedron,vertex figure ofgax0.587785
gikepy4Dgreat-icosahedral pyramid, vertex cap ofgax0.618034
gikkiv datapixady4Dgreat skewverted ditrigonary prismatohexacosadishecatonicosachoron2.013884
gikkiv datixathi4Dgreat skewverted ditrigonary hexacosatrishecatonicosachoron2.013884
gikkiv pacoca (old: sic vacpeca)3Dgreat skewverted prismatocubaticubatiapeiratic honeycomb, small skewverted cubatiprismated cubatiapeiratic honeycomb
gikkivcadach3Dgreat skewverted cubatiapeiroducubatic honeycomb
gikrid3Dgreat chirorhombidodecahedron,compound of 6stip0.725530
giku4Dgike-based ursachoron0.965407
gikvacadint5Dgreat skewverted cellidispenteractitriacontiditeron1.429298
gikviphado4Dgreat skewverted prismatohexadecadisoctachoron1.414214
ginnont5Dgreat penteractipenteractitriacontiditeron1.021221
ginnontip6Dginnont prism1.137055
gipaht4Dgreat prismated demitesseractic tetracomb, runcicantitruncated hexadecachoric tetracomb
gipbin5Dgreat prismated biprismatopenteract0.914214
...4Dvertex figure ofgreat prismated biprismatopenteract0.837186
gipdohiny4Dgreat pental dishecatonicosaintercepted hecatonicosachoron0.726543
gipe4Dgreat-icosahedron prism0.771681
giphado4Dgreat prismatohexadecadisoctachoron1.082392
giphatit4Dgreat prismated demitesseractic tetracomb, great diprismatodemitesseractic tetracomb, steriruncicantic tesseractic tetracomb
giphiddix4Dgreat prismatohecatonicosadishexacosachoron1.624598
giphidy4Dgreat prismated hecatonicosadishecatonicosachoron1.348948
giphihix4Dgreat prismatohecatonicosahecatonicosahexacosachoron1.893038
giphin5Dgreat prismatedhemipenteract, steriruncicanticpenteract3.259601
giphixhi4Dgreat prismatohecatonicosihexacosihecatonicosachoron2.920251
gipidded3Dhyperbolic great prismatodisdodecahedral honeycomb, hyperbolic omnitruncated order 5 dodecahedral tesselation3.176503i
gipiddih3Dhyperbolic great prismatodisicosahedral honeycomb, hyperbolic omnitruncated order 3 icosahedral honeycomb4.308399i
gippapivady4Dgreat pentagrammal antiprismatoverted dishecatonicosachoron0.726543
gippic4Dgreat prismatotetracontoctachoron, omnitruncatedicositetrachoron5.169905
gippiccup5Dgreat-prismatotetracontoctachoron prism, omnitruncated-icositetrachoron prism5.194028
gippich (old: otch)3Dgreat prismated cubic honeycomb, omnitruncated cubic honeycomb
gippict4Dgreat prismated icositetrachoric tetracomb, runcicantitruncated icositetrachoric tetracomb
gippid4Dgreat prismatodecachoron, omnitruncatedpentachoron, Voronoi cell oflattice A4*,permutochoron of 5 elements2.236068
gippiddip5Dgreat-prismatodecachoron prism2.291288
gippin5Dgreat prismatedpenteract, runcicantitruncated penteract4.371952
gippit5Dgreat prismatedtriacontiditeron, omnitruncatedhemipenteract3.872983
gippitip6Dgreat-prismated-triacontiditeron prism3.905125
gippittit4Dgreat prismated tesseractic tetracomb, great diprismatotesseractic tetracomb, runcicantitruncated tesseractic tetracomb
gippix5Dgreat prismatedhexateron, runcicantitruncated hexateron2.581989
gippixady4Dgreat prismatohexacosadishecatonicosachoron1.207883
gippixhihy4Dgreat prismatohexacosihecatonicosihecatonicosachoron1.021064
giprapivady4Dgreat pentagonal retroprismatoverted dishecatonicosachoron1.902113
gipriphi4Dgreat pseudorhombated prismatohecatonicosachoron0.799575
...4Dgipriphi+600 2thah (?)0.799575
gipthi4Dgreat prismatotriakishecatonicosachoron3.531591
gipti4Dgreat prismatotriakisicositetrachoron1.938391
giqragashi4Dgreat quasirhombated grand stellated hecatonicosachoron2
girc4Dgreat retrotetracontoctachoron0.765367
gircaptint (old: grecaptint)5Dgreat retrocelliprismatotruncated penteractitriacontaditeron1.949424
girco3Dgreat rhombicuboctahedron (butnotquerco), truncatedcuboctahedron, omnitruncatedoctahedron, omnitruncatedcube2.317611
gircope, K-4.1254Dgreat-rhombicuboctahedron prism2.370932
gird3Dgreat rhombidodecahedron0.716891
...3Dgird+12{10/4} (?)0.716891
...3Dgird+20{6/2} (?)0.716891
girdip4Dgreat-rhombidodecahedron prism0.874032
girdo4Dgreat rhombic disoctachoron0.765367
girfaddic4Dgreat retrofrustic distetracontoctachoron1.414214
girfix4Dgreat rhombated faceted hexacosachoron7.404918
girfixady4Dgreat retrofrustary hexacosidishecatonicosachoron2.236068
girfixthi4Dgreat retrofrustic hexacositrishecatonicosachoron2.236068
girfthi4Dgreat retrofrustary trishecatonicosachoron2.236068
...3Dvertex figure ofgreat retrofrustary trishecatonicosachoron0.816497
girgikaike4Dgreat retrogikaike1
girhax6Dgreat rhombatedhemihexeract, cantitruncated demihexeract, runcicantichexeract3.278719
girhin5Dgreat rhombatedhemipenteract, cantitruncated demipenteract, runcicanticpenteract2.761340
girjak6Dgreat rhombatedicosiheptaheptacontidipeton3.605551
girn5Dgreat rhombatedpenteract, cantitruncated penteract3.563671
girpdi4Dgreat rhombiprismic disicosatetrachoron1.938391
girpdo4Dgreat rhombiprismatodisoctachoron1.174172
girpith4Dgreat rhombiprismated tesseractihexadecachoron1.082392
girpixhi4Dgreat rhombiprismic hexacosahecatonicosachoron1.021064
girsid3Dgreat (inverted) retrosnub icosidodecahedron, azathoth
girsiddip4Dgreat-(inverted)-retrosnub-icosidodecahedron prism
gisdid3Dgreat snub dodekicosidodecahedron, shub-niggurath0.707107
gisdiddip4Dgreat-snub-dodekicosidodecahedron prism
gisdiddit6D(gisdid,gisdid)-duotegum,gisdid duotegum,tegum product of 2great snub dodekicosidodecahedra0.707107
gisdipthi4Dgreat stellated dipental trishecatonicosachoron1.328131
...4Dgishi+gashi (?)0.618034
gishi, gspD4Dgreat stellatedhecatonicosachoron, greatened stellated polydodecahedron0.618034
giship3Dtristrophic heptagrammic prism, heptagrammic prism of winding number 3, great heptagrammic prism, great stellated heptagonal prism0.716257
gishitte4Dgreat stellated hecatonicosachoric tetracomb0.476925
gisid3Dgreat inverted snub icosidodecahedron, great vertisnub icosidodecahedron, cthulhu
gisiddip4Dgreat-inverted-snub-icosidodecahedron prism
gisp4Dgreat swirlprism0.618034
gissed3Dgreat invertisnub dodecahedron,compound of 6starp0.587785
gissi3Dgreat snub icosahedron,compound of 10oct (butnotsi)0.707107
gissid3Dgreat stellateddodecahedron, tri-stellahedron0.535233
...4Dtallergreat stellated dodecahedron atopsmall stellated dodecahedron0.662791
gissidagid, gissid || gid4Dgreat stellated dodecahedron atopgreat icosidodecahedron,great stellated dodecahedral cupola0.692924
gissidagike4Dgreat stellated dodecahedron antiprism,great icosahedron antiprism, tallergreat stellated dodecahedron atopgreat icosahedron0.662791
gissidasissid4Dshallowergreat stellated dodecahedron atopsmall stellated dodecahedron0.618034
gissiddip4Dgreat-stellated-dodecahedron prism0.732444
gissidpy4Dgreat-stellated-dodecahedral pyramid, vertex cap ofgaghi0.591923
gissidragike4Dgreat stellated dodecahedron retroprism,great icosahedron retroprism, narrowergreat stellated dodecahedron atopgreat icosahedron0.618034
gistic4Dgreat stellated icositetrachoron,compound of 6tes,compound of 2gico1
git thixady4Dgreat tritrigonal hecatonicosihexacosidishecatonicosachoron1.136572
githawro3Dgreat triangular hebesphenorotunda
gitphi4Dgreat tripesic hecatonicosachoron0.874032
gitpodady4Dgreat (intersected) tripesic dodecahedronary dishecatonicosachoron1
gittifcoth4Dgreat tesseractifaceted cubitesseractihexadecachoron0.890446
gittith4Dgreat tesseractitesseractihexadecachoron0.890446
gittithip5Dgreat-tesseractitesseractihexadecachoron prism1.021221
gixathi4Dgreat hexacositriakishecatonicosachoron3.804226
gixhi4Dgreat hexacosihecatonicosachoron1.244649
gixhidy4Dgreat hexacosihecatonicosadishecatonicosachoron1.464888
gixhihy4Dgreat hexacosihecatonicosihecatonicosachoron0.763932
gixipady4Dgreat hexacosiprismatodishecatonicosachoron1.624598
gloptin5Dgreat lapidoprismatotruncated penteract1.416813
gnappoth4Dgreat spinoprismatotesseractihexadecachoron0.890446
gobath3Dgreat biambotetrahedral honeycomb
gocad (old: gohad)5Dgreat cellateddodecateron (great hedrated dodecateron), omnitruncatedhexateron, Voronoi cell oflattice A5*,permutoteron of 6 elements2.958040
gocadip6Dgreat-cellated-hexateron prism3
gocap4Dgreat cycloantiprism1
gocax6Dgreat cellatedhexeract5.865108
gocco3Dgreat cubicuboctahedron0.736813
goccoa cotco4Dgreat cubicuboctahedron atopcubotruncated cuboctahedron1.414214
goccoasocco4D(degenerate)gocco atopsocco∞   i.e. flat in euclidean space
goccope4Dgreat-cubicuboctahedron prism0.890446
goccopen7D(gocco,pen)-duoprism0.971027
gocog6Dgreat cellatedhexacontitetrapeton, steriruncicantitruncatedhemihexeract, omnitruncatedhemihexeract5.244044
gocypapit5Dbitruncated pentachoric tetracomb, great cycloprismated pentachoric tetrachomb, grand prismatodispentachoric tetracomb
gocyropit4Dgreat cyclorhombated pentachoric tetrachomb, great truncated-pentachoric tetracomb, cantitruncated pentachoric tetrachomb
...4Dgofix+gishi+120gid (?)0.618034
gofix, gpI4Dgreat icosahedral hecatonicosachoron, great facetedhexacosichoron, greatened polyicosahedron0.618034
gofixa quipdohi5D(degenerate)gofix atopquipdohi∞   i.e. flat in euclidean space
gofixu5Dgofix-based ursateron1.008123
gogishi, gaspD4Dgreat grand stellatedhecatonicosachoron, greatened aggrandized stellated polydodecahedron0.540182
gogishiagax5Dgreat grand stellated hecatonicosachoron antiprism,grand hexacosachoron antiprism, tallergreat grand stellated hecatonicosachoron atopgrand hexacosachoron0.667731
gogiship5Dgreat-grand-stellated-hecatonicosachoron prism0.736068
gogishiragax5Dgreat grand stellated hecatonicosachoron retroprism,grand hexacosachoron retroprism, narrowergreat grand stellated hecatonicosachoron atopgrand hexacosachoron0.636010
goh8DGosset octacomb 52,1,Delone complex oflattice E8
gohi, gpD4Dgreathecatonicosachoron, greatened polydodecahedron1.618034
gohihix4Dgreat hecatonicosihecatonicosihexacosachoron1.464888
gohiny4Dgreat hecatonicosintercepted hecatonicosachoron0.661585
gohip5Dgreat hexacosachoron prism1.693527
gohitte4Dhyperbolic great-hecatonicosachoral tetracomb0.393076i
gokvactaden5Dgreat skewverted cellitriacontadiadispenteract1.429298
gondip4Dgreat octagonal spinoduoprism0.890446
gook8Dgreat octeractiocteractidiacosipentacontahexazetton1.338990
gopam (old: gakpam)6Dgreat prismatedpentacontitetrapeton, (great heptaheptacontidiprismated pentacontitetrapeton), omnitruncated pentacontitetrapeton, omnitruncatedicosiheptaheptacontidipeton6.244998
gopamp7Dgreat-prismated-pentacontitetrapeton prism6.264982
gophax6Dgreat prismateddemihexeract, steriruncicantichexeract4.092676
gopog6Dgreat prismatedhexacontitetrapeton, runcicantitruncated hexacross3.872983
goquidipdy4Dgreat quasidisprismatodishecatonicosachoron6.566933
gorcpit5Dgreat retrocelliprismated triacontiditeron1.102028
gorcrin5Dgreat retrocelligreat rhombated penteract2.143163
gosid3Dgreat snub icosidodecahedron, tsathoggua
gosiddip4Dgreat-snub-icosidodecahedron prism
gososaz7Dgreat hepteractihepteractihecatonicosoctaexon1.242133
gossa2Dgreat squarisquariapeirogonal tiling
gotaf6Dgreat teratedtetradecapeton, omnitruncatedheptapeton, Voronoi cell oflattice A6*,permutopeton of 7 elements3.741657
gotafip7Dgreat-terated-tetradecapeton prism3.774917
gotanq (old: gotalq)7Dgreat teratedhecatonicosihexapentacosiheptacontihexaexon, omnitruncatedGosset polyexon 32,1, great teratedpentacontihexapentacosiheptacontihexaexon, omnitruncatedGosset polyexon 21,3, great teratedpentacontihexahecatonicosihexaexon, omnitruncatedGosset polyexon 12,39.987492
gotaxog6Dgreat teratedhexeractihexacontatetrapeton6.293378
gotaz7Dgreat terated hecatonicosoctaexon, great terated heptacross6.745369
gotdatixhi4Dgreat toroidoditrigonary hexacosihecatonicosachoron1.732051
gotditpix4Dgreat toroidoditrigonary prismatohexacosichoron1.732051
gotfipte4Dgreat terifaceted pentachoric tetracomb0.568286
gotto4Dgreat trisoctachoron, great triakisoctachoron1.224745
...2DGott'ssnic-based pseudopolyhedron
goxaxog6Dgreat hexeractihexeractihexacontitetrapeton1.137055
goxaxogip7Dgoxaxog prism1.242133
goxeb8Dgreat exi-octadecazetton,permutozetton of 9 elements5.477226
grad tathi4Dgreat retroditetrahedronary trishecatonicosachoron1.414214
graggix4Dgreat rhombated grand hexacosachoron1.658546
graghi4Dgreat rhombatedgrand hecatonicosachoron4.550627
grahi4Dgreat rhombatedhecatonicosachoron, cantitruncated hecatonicosachoron11.252107
grahip (old: grahipe)5Dgreat-rhombated-hecatonicosachoron prism, cantitruncated-hecatonicosachoron prism11.263210
graht2Dgreat rhombihexagonal tiling
gram (old: gakbram)6Dgreat rhombatedpentacontitetrapeton, (old: great heptacontiduo-birhombated pentacontitetrapeton), cantitruncated pentacontitetrapeton5
graphi4Dgrand retropental hecatonicosachoron0.726543
grassid3Dgreat rhombisnub dodecahedron,compound of 6stiddip0.794963
grath3Dhyperbolic great rhombatedorder 6 tetrahedral honeycomb3.316625i
gratoh3Dgreat rhombated tetrahedral-octahedral honeycomb, cantitruncated alternated cubic honeycomb, cantitruncated tetrahedral-octahedral honeycomb, runcicantic cubic honeycomb
grawv ditathi4Dgreat retrosphenoverted ditrigonary triakishecatonicosachoron2.093315
grawv hidy4Dgreat retrosphenoverted hecatonicosadishecatonicosachoron1.589926
grawv hixhi4Dgreat retrosphenoverted hecatonicosihexacosihecatonicosachoron1.513868
grawvathi4Dgreat retrosphenoverted triakishecatonicosachoron2.572554
grawvixady4Dgreat retrosphenoverted hexacosadishecatonicosachoron2.036148
grich3Dgreat rhombated cubic honeycomb, cantitruncated cubic honeycomb
grico4Dgreat rhombatedicositetrachoron, cantitruncated icositetrachoron4.299451
..., grico || gippic5D(degenerate)grico atopgippic∞   i.e. flat in euclidean space
gricoa (old: gricoalgrico)5Dgreat-rhombated-icositetrachoron alterprism,great-rhombated-icositetrachoron atop alternategreat-rhombated-icositetrachoron4.311477
gricope (old: gripe)5Dgreat-rhombated-icositetrachoron prism, cantitruncated-icositetrachoron prism4.328427
gricot4Dgreat rhombated icositetrachoric tetracomb, great prismatodisicositetrachoric tetracomb
grid3Dgreat (convex) rhombicosidodecahedron (i.e.notqrid), truncatedicosidodecahedron, omnitruncatedicosahedron, omnitruncateddodecahedron3.802395
..., xFoFx3xxxxx5xofox&#xt   (F=ff=x+f)4Dbilunabirotundic great rhombicosidodecahedron prism
gridaphi4Dgreat retroinverted dodecahedronary prismatohecatonicosachoron1
griddip, K-4.1504Dgreat-rhombicosidodecahedron prism3.835128
griddoh3Dhyperbolic great rhombated (order 4) dodecahedral honeycomb, hyperbolic cantitruncated order 4 dodecahedral honeycomb3.466586i
gridixhi4Dgreat retroinverted dodecahedronary hexacosahecatonicosachoron1
gridtathi4Dgreat retroinverted ditetrahedronary trishecatonicosachoron1.414214
grih3Dhyperbolic great rhombated order 3 icosahedral honeycomb, hyperbolic cantitruncated order 3 icosahedral honeycomb3.601065i
gril6Dgreat rhombatedheptapeton, cantitruncated heptapeton2.104417
grip4Dgreat rhombatedpentachoron, cantitruncated pentachoron1.843909
gripa (old: gripalgrip)5Dgrip alterprism,grip atop invertedgrip, medialspid-first segment ofspat1.870829
gripady4Dgreat rhombiprismic dishecatonicosachoron1.207883
gripagippid5Dgrip atopgippid,grip-first cap ofcograx2.327373
gripech3Dhyperbolic great rhombated order 5 cubic honeycomb, hyperbolic cantitruncated order 5 cubic honeycomb3.185991i
griphi4Dgreat retropental hecatonicosachoron1.175571
gripped3Dhyperbolic great rhombated order 5 dodecahedral honeycomb, hyperbolic cantitruncated order 5 dodecahedral honeycomb2.456999i
grippip5Dgreat-rhombated-pentachoron prism1.910497
griso3Dgreat rhombisnub octahedron,compound of 4hip1.118034
grit4Dgreat rhombatedtesseract, cantitruncated tesseract3.005916
gritta gidpith5Dgrit atopgidpith,grit-first segment ofcogrin3.988340
grittip5Dtruncated-tesseract prism, central segment ofprin3.047217
grittit4Dgreat prismatotesseractic tetracomb, cantitruncated tesseractic tetracomb
grix4Dgreat rhombatedhexacosachoron, cantitruncated hexacosachoron9.124101
..., grix || prix5D(degenerate)grix atopprix∞   i.e. flat in euclidean space
grixip5Dgreat-rhombated-hexacosachoron prism9.137791
grog6Dgreat rhombihexacontitetrapeton, cantitruncated hexacross2.645751
groh3Dgreat rhombihexahedron0.736813
...3Dgroh+8{6/2} (?)0.736813
grohp4Dgreat-rhombihexahedron prism0.890446
groptin5Dgreat retroprismatotruncated penteract1.416813
grotazt2Dhyperbolic great rhombitriapeirogonal tiling, hyperbolic omnitruncated trigonal-horocyclic tiling, hyperbolic truncated triapeirogonal tiling2.397916i
grotehat2Dhyperbolic great rhombitetrahexagon tiling, hyperbolic order 6 omnitruncated square tiling, hyperbolic order 4 omnitruncated hexagon tiling2.474067i
grotepet (old: opeat)2Dgreat rhombitetrapentagonal tiling, omnitruncated pentagonal tiling, hyperbolic omnitruncated tetrapentagonal tiling3.121470i
grothaph (old: otathaph)3Dgreat rhombitrihexagonal prismatic honeycomb, omnitruncated triangular-hexagonal prismatic honeycomb
grothat (old: othat)2Dgreat rhombitrihexagonal tiling, omnitruncated trihexagonal tiling
grothet (old: othet)2Dhyperbolic great rhombitruncated triheptagonal tiling, hyperbolic omnitruncated triheptagonal tiling4.779184i
grotoct (old: otoct)2Dhyperbolic great rhombated trioctagonal tiling, hyperbolic omnitruncated trioctagonal tiling3.699185i
grox6Dgreat rhombihexeract, cantitruncated hexeract4.045239
gu7Dgee-based ursaexon,vertex figure of s3s4o3o3o3o3o4o1.144123
gudap (old: gedap)4Dgreat duoantiprism, (old: great double antiprism – butnot:great antiprism)1
guhsa (old: xhaf)7Dhexacontitetrahemihepteract, hexacontitetrahemitetradecaexon0.707107
guph7Dgreat petatedhexadecaexon, hexipentisteriruncicantitruncatedoctaexon, omnitruncated octaexon,permutoexon of 8 elements4.582576
gupofy8Dgreat petateddischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton17.606817
guti4Dgreat tetrakisicositetrachoron2.326846
gwav ditathi4Dgreat sphenoverted ditrigonary triakishecatonicosachoron2.036148
gwavathi4Dgreat sphenoverted triakishecatonicosachoron1.027486
gwavixady4Dgreat sphenoverted hexacosadishecatonicosachoron0.799575
gyautisdip4Dgyro-augmented3-4-duoprism...
gybadrid, J823Dgyrate(d) bidiminished rhombicosidodecahedron2.232951
gybef, J263Dgyrobifastegium
gybeffip4Dgybef prism
gyeditoh3Dgyroelongated ditetrahedral-octahedral honeycomb
gyepabro, J483Dgyroelongated pentagonal birotunda
gyepcu, J243Dgyroelongated pentagonal cupola
gyepcuro, J473Dgyroelongated pentagonal cupolarotunda
gyepibcu, J463Dgyroelongated pentagonal bicupola
gyepip, J113Dgyroelongated pentagonal pyramid, diminished icosahedron
gyepipa pero, K-4.1404Dgyroelongated pentagonal pyramid atoppentagonal rotunda3.077684
gyepippip4Dgyroelongated-pentagonal-pyramid prism1.074481
gyepro, J253Dgyroelongated pentagonal rotunda
gyerich3Dparallellythat elongatedgyrich
gyescu, J233Dgyroelongated square cupola
gyesp, J103Dgyroelongated square pyramid
gyesqidpy, J173Dgyroelongated square dipyramid
gyesquibcu, J453Dgyroelongated square bicupola
gyetac5Dgyroelongatedtriacontaditeron, parabiapiculateddemipenteract...
gyetaph3Dgyroelongated triangular-prismatic honeycomb
gyetcu, J223Dgyroelongated triangular cupola
gyetibcu, J443Dgyroelongated triangular bicupola
gyetoh3Dgyroelongated tetrahedral-octahedral honeycomb, gyroelongated alternated cubic honeycomb
gypasp4Dgreat pyramidic swirlprism0.618034
gyprip4Dgyratedprip1.612452
gyquerco (alt.: rers quigybcu)3Dinverto-elongated retrograde square gyrobicupola, gyrated quasirhombicuboctahedron, pseudo great rhombicuboctahedron, retroelongated retrosquare gyrobicupola0.736813
gyrich3Dgyratedrectified cubical honeycomb
gyrid, J723Dgyrated rhombicosidodecahedron2.232951
gyspid (alt: tetacobcu)4Dgyrated small prismatodecachoron, orthobicupola of runcinated pentachoron,tetaco orthobicupola1
gytoh3Dgyrated tetrahedral-octahedral honeycomb, gyrated alternated cubic honeycomb
gytoph3Dgyrated-bifastegium honeycomb
gytoph3Dgyrated triangular prismatic honeycomb

H

hachon3Dhyperbolic order 6cubical honeycomb0i
haco (old: hicco)5Dhexagon cuboctahedron duoprism1.414214
hacube (old: hiccube)5Dhexagon cube duoprism1.322876
haddet4Ddemidistesseract, hexadecadistesseract,compound of 2hex0.707107
hadedip4Dhexagon - decagon duoprism1.902113
hadoe5Dhexagon - dodecahedron duoprism1.721489
haf, K-4.464Dhexagonal antifastegium, hexagon -hap wedge, {6} || gyrohip1.130454
hagippid6Dhexagon -great-prismated-decachoron duoprism2.449490
hagippiddip7Dhexagon - great-prismated-pentachoron duoprism prism2.5
hagippit7Dhexagon -great-prismated-triacontiditeron duoprism4
hagirco (old: higgirco)5Dhexagon great-rhombicuboctahedron duoprism2.524147
hagocad7Dhexagon -great-cellated-dodecateron duoprism3.122499
hagrid5Dhexagon - great-rhombicosidodecahedron duoprism3.931692
hagy gircope4Dhexa-gyro-augmentedgircope
hahip (old: hiddippip)5Dhexagon hexagonal-prism duoprism, hexagon-hexagon duoprismatic prism1.5
han5Dhexadecapenteract,vertex figure ofdaj0.790569
haop (old: hodippip)5Dhexagon octagonal-prism duoprism, hexagon-octagon duoprismatic prism1.719624
hap, 6-ap3Dhexagonal antiprism1.087664
happip, K-4.534Dhexagonal-antiprism prism1.197085
haprojak6Ddemiprismatorhombatedicosiheptapeton3.559026
haquitco5Dhexagon - quasitruncated-cuboctahedron duoprism1.459000
harjak (old: trojak)6Ddemirectifiedicosiheptaheptacontidipeton (trirectified icosiheptaheptacontidipeton)2.160247
hasirco (old: hissirco)5Dhexagon small-rhombicuboctahedron duoprism1.719624
hasrid5Dhexagon - small-rhombicosidodecahedron duoprism2.446644
hatet (old: hittet, alt. hipdaw)5Dhexagon-tetrahedron duoprism, hexagon duofastegium,hipdisphenoid1.172604
hatha2Dhexaapeirogonaltruncated hexaapeirogonal tiling
hatho4Dhemitesseractihemioctachoron0.707107
hati5Dhexagon - truncated-icosahedron duoprism2.672186
hatic (old: hittic)5Dhexagon truncated-cube duoprism2.040640
hatico6Dhexagon - truncated-icositetrachoron duoprism2.828427
hatid5Dhexagon - truncated-dodecahedron duoprism3.133309
hatiph3Dhemiated triangular-prismatic honeycomb, cell-alternatedtriangular-prismatic honeycomb
hatoe (old: hittoe)5Dhexagon truncated-octahedron duoprism1.870829
hatope6Dhexagon - truncated-octahedron duoprismatic prism1.936492
hatricu5Dhexagon-tricu duoprism,trip-first half ofhaco1.414214
hatut (old: hittut)5Dhexagon truncatet-tetrahedron duoprism1.541104
hau gircope4Dhexa-augmentedgircope
hau ticcup4Dhexa-(ortho-)augmentedticcup
haucope4Dhexa-augmentedcope
hauhocto8Dhexadeca-augmentedhemiocteract...
hautope4Dhexa-augmentedtope
hawmco, J893Dhebesphenomegacorona
...4Dexternal blend of thehebesphenomegacorona-prism and acube-pyramid,cubic-pyramid-augmentedhebesphenomegacorona-prism
hax6Dhemihexeract,vertex figure oflaq,Gosset polytope 13,1, equatorial cross-section ofgee-firstnaq0.866025
haxa cytedbrag7Dhax atopcytedbrag1.322876
haxabrag7Dhax-first monostratic cap oflin,hax atopbrag1.322876
haxabrox7Dhax atopbrox,hax-first cap ofrolaq1.732051
haxarag7Dhemihexeract atoprectified hexacontitetrapeton, vertex-first subsegment ofpentacontihexapentacosiheptacontihexaexon1
haxesc8D(degenerate)demihexaracticscalene, line atop fully orthogonaldemihexaract∞   i.e. flat in euclidean space
haxh6Dhemihexeractic pentacomb,Delone complex oflattice D6
haxip7Dhemihexeractic prism,vertex figure ofrinquoh1.060660
haxpy7Dhemihexeractic pyramid, vertex pyramid oflaq1
haxt7Ddemihexeractic (line-)tegum,demihexeracticbipyramid...
hazt2Dhyperbolic hexa-apeirogonal tiling0.577350i
he (old: ache)7Dhexadecaexon, trirectified octaexon, equatorial cross-section of (vertex first) 1/q-octo,Gosset polytope 03,31
heat2Dhyperbolic order 3 heptagonal tiling1.742610i
heath3Dhyperbolic o3o3o7x tesselation,heat honeycomb1.071823i
hede10Ddemi-dekeract,Gosset polytope 17,11.118034
hedhon3Dhyperbolic order 6dodecahedral honeycomb0i
hedip4Dheptagonal-heptagonal duoprism1.629715
hedjak6Dheptadiminishedjak, square ||hin0.816497
hehad5Dhexadecahemidecateron,vertex figure ofthox0.707107
hehah7Dhexadecahemihexadecaexon1
hejak6Ddemifiedicosiheptaheptacontidipeton1.632993
hejaka7Dhejak alterprism,hejak atop alternatehejak1.658312
henne9Ddemi-enneract,Gosset polytope 16,11.060660
hep3Dheptagonal prism1.256179
hept7Dhepteract, tetradecaexon, 7Dmeasure-polytope (γ7), geozett(id)1.322876
hepth7Dhepteractic heptacomb, 7Dhypercubical honeycomb (δ7)
hesa (old: hiss)7Dhemihepteract,vertex figure ofbay,Gosset polytope 14,10.935414
hesapy8Dhemihepteractic pyramid, vertex pyramid ofbay1.414214
hetoh3Dhyperbolic x3o3o7o tesselation, order 7 tetrahedral honeycomb0.376651
hetrat2Dhyperbolic order 7 triangular tiling0.873057i
...4Dhex+8oct (?)0.707107
hex, K-4.2 (alt: octit, trapt)4Dhexadecachoron,tetracross (β4), orthoplex, hemitesseract, hemioctachoron, 16-cell, aeroter(id),tetrahedral antiprism,vertex figure oftac, (line-)octahedral tegum, (line-)trigonal-antirprismatic tegum,Gosset polytope 11,1, 8-3-stepprism,lattice C4 contact polytope (span of its small roots), equatorial cross-section of vertex-firsttac0.707107
..., hex || icope || rit6Dhex-first quarter-lune ofbrag1.224745
hexaco5Dhexadecachoron atopcuboctahedron, 0.147584-lune ofrectified triacontiditeron,hexadecachoron-firstlune ofrectified triacontiditeron1
hexaf (alt. hexalhexip)6Dhexadecachoral alterfastegium,hex atop gyratedhexip,hex-firstrotunda ofhax0.866025
hexah3Dhyperbolic order 3hexagonal-tiling honeycomb1.414214i
hexaico alrittric6D(hex,ico, alt.rit)-trigonic1.290994
hexaico, hex || ico5Dhexadecachoron-firstrotunda ofrectified triacontiditeron,hexadecachoron atopicositetrachoron, rectifiedhexadecachoron-pyramid1
hexaicope6Dhexadecachoron atopicositetrachoron-prism1.224745
hexal hesa8Dhex atop alternatedhesa,hex-first cap ofcodify1
hexal trahex7Dhex atop gyratedtrahex,hex-first cap ofhesa0.935414
hexalhax7Dhex atop alternatehax0.866025
hexalrit5Dhex atop gyratedrit,hex-first cap ofsiphin1.274755
hexaoctaco tettic6D(hex,octaco)-disphenoid, (hex,octaco)-duopyramid, (oct,co,hex)trigonic, (tet,oct, dualtet,co)tetrahedric1
hexarat6Dhex atoprat,hex-first half oftedrag1
hexarit5D(degenerate)hex atoprit∞   i.e. flat in euclidean space
hexasc6Dhexadecachoricscalene,hexadecachoron-pyramid pyramid, line atop fully orthogonalhexadecachoron, 1/4-lune ofhexacontatetrapeton0.707107
hexasidpith5D(degenerate)hex atopsidpith∞   i.e. flat in euclidean space
hexat2Dhexagonal tiling,Voronoi complex of hexagonallattice A2
...3Dhexatipblend
hexathex5D(degenerate)hex atopthex∞   i.e. flat in euclidean space
hexatip3Dhexagonal tiling prism
hexcopedaw (alt.: hexorcope)6D(hex,cope)-disphenoid, (hex,cope)-duopyramid,tetrahedral antiprism atop axis-orthogonalcuboctahedron prism1.224745
hexdex4Dhexadecadiminishedhexacosachoron1.618034
hexdip8Dhexadecachoron duoprism1
hexepe8Dhexadecachoricpennene,hexadecachoron-pyramid pyramid-pyramid-pyramid,tetrahedron atop fully orthogonalhexadecachoron, 1/4-lune ofdiacosipentacontahexazetton0.707107
hexete7Dhexadecachorictettene,hexadecachoron-pyramid pyramid-pyramid, triangle atop fully orthogonalhexadecachoron0.707107
hexip5Dhexadecachoron prism,vertex figure ofrag, equatorial cross-section ofhex-firsthax0.866025
hexipaco6Dhexip atopco1
hexipaico6Dhexip atopico, diminished 1/4-lune ofrag1
hexippy6Dhexip pyramid, vertex pyramid ofrag1
hexpy5Dhexadecachoral pyramid, vertex-firstrotunda oftriacontiditeron0.707107
hext4Dhexadecachoric tetracomb, demitesseractic tetracomb,Delone complex of body-centered tesseracticlattice,Gosset polytope 11,1,1
hextes8Dhexadecachoron-tesseract duoprism1.224745
hextum5Dhex-basedtutsatope,hex-based tutism,hex-firstrotunda oftot,truncation ofhexpy1.581139
hexu5Dhexadecachoron-based ursateron,hex-basedursulate,vertex figure ofs3s4o3o3o4o1.144123
hi, pD4Dhecatonicosachoron, 120-cell, dodecacontachoron, twelftychoron, cosmochoron, dodecaplex, polydodecahedron, hyperdodecahedron3.702459
...4Dhi dimpled in by 120ikadoes...
hiarahi, hi || rahi5D(degenerate)hi atoprahi∞   i.e. flat in euclidean space
hibbit4Dhexagonal biprismated tetracomb, hexagonal duoprismatic tetracomb, hexagonal tiling duocomb,Voronoi complex of bihexagonallattice A2×A2
hicu3Dhexagonal cupola∞   i.e. flat in euclidean space
hid5Dhexagon icosidodecahedron duoprism1.902113
hidbrag6Dhexadeca-diminishedbrag,tegum sum of 2 antialignedoctcoes1.224745
hiddip4Dhexagonal-hexagonal duoprism, Voronoi cell oflattice A2×A21.414214
hidhi4Dhecatonicosa-diminishedhecatonicosachoron3.702459
hidicau pretasto4Dhexadeca-diminishedicositetra-augmented pentagonorhombic-trisnub-trisoctachoron
hidip8Dhecatonicosachoron duoprism5.236068
hidlin7Dhexadeca-diminishedpentacontihexahecatonicosihexaexon1.322876
hihexah3Dhyperbolic order 6hexagonal-tiling honeycomb0i
hihexat2Dhyperbolic order 6 hexagonal tiling0.353553i
hihiquatady4Dhecatonicosihecatonicosiquasitruncated dishecatonicosachoron3.605551
hike5Dhexagon icosahedron duoprism1.380039
hiktut3Dhexakis truncated tetrahedron1.172604
hin5Dhemipenteract, demipenteract,hemitesseractic gyroprism,tetrahedralaltersquarism,vertex figure ofjak,Gosset polytope 12,10.790569
hinaco6Dhemipenteract atopcuboctahedron1
hinaf, hin || alt. hinnip7Dhemipenteractic alterfastegium,hin atop alternatehinnip,hin-firstrotunda ofhesa0.935414
hinaicarit tettic7D(hin,icarit)-disphenoid, (hin,icarit)-duopyramid, (gyrohex, alt. gyrohex,ico,rit)tetrahedric1.322876
hinanit6Dhin atopnit,hin-first cap ofrojak1.290994
hinanitarita6D(demipenteract,penteractitriacontiditeron,rectified-tesseractic alterprism) -lace tower1.290994
hinaratip7Ddemipenteract atoprectified-triacontiditeron prism,hin-first cap oflin1.322876
hinarin6Ddemipenteract atoprectified penteract,demipenteract-first cap ofdemified icosiheptaheptacontidipeton1.632993
hinasiphin6Dhin atopsiphin,hin-first cap ofsochax1.322876
hinatedrat6Dhin atoptedrat1
hinhi4Dhecatonicosintercepted hecatonicosachoron2.802517
hinnip6Dhemipenteractic prism,vertex figure ofranq0.935414
hinnipa ratip7Ddemipenteractic-prism atoprectified-triacontidiateron-prism,hinnip-first half ofmo-prism1.118034
hinnit4Dhexadekintercepted tesseract1.224745
hinoh5Dhemipenteractic pentacomb, alternated penteractic pentacomb,Delone complex oflattice D5
hinpy6Ddemipenteractic pyramid, vertex pyramid ofjak0.816497
hinro (alt.: hinarat)6Ddemipenteracticrotunda,hin-first half ofmo,hin atoprat1
hinsc7Ddemipenteracticscalene,demipenteractic-pyramid pyramid, line atop fully orthogonaldemipenteract0.866025
hint6Ddemipenteractic (line-)tegum,demipenteractic dipyramid...
hinu6Dhin-based ursapeton1.287166
hip3Dhexagonal prism, Voronoi cell of unit-stacked hexagonallattice1.118034
hipat2Dhyperbolic order 6 pentagonal tiling0.393076i
hipe5Dhecatonicosachoron prism3.736068
hiph3Dhexagonal prismatic honeycomb,Voronoi complex of unit-stacked hexagonallattice
hippy, 6pyr3D(degenerate) hexagonal pyramid∞   i.e. flat in euclidean space
hippyp4Dhexagon-pyramidal prism, line ||hip∞   i.e. flat in euclidean space
hirki3Dhemirhombichiro-icosahedron,compound of 5thah0.707107
hirlaq7Ddemirectifiedpentacontihexapentacosiheptacontihexaexon2.958040
hisquat2Dhyperbolic order 6 square tiling0.5i
hisquippy5Dhexagon-squippy douprism, half ofhoct1.224745
histodip4Dhexagon - octagram duoprism1.137055
hit5Dhexadecateron0.790569
...4Dvertex figure ofhexadecateron0.774597
hitte4Dhyperbolic (order 3)hecatonicosachoric tetracomb2.301105i
hittip6Dhexagon-hexagon-hexagon-triprism1.732051
hitwadip4Dhexagon - dodecagon duoprism2.175328
hix5Dhexateron, 5Dsimplex (α5), pyropet(id),pentachoral pyramid, regulartet-scalene, regular triangle-tettene, regular line-pennene, regular (point-)hixene, digonal gyrotrigonism,vertex figure ofhop,Gosset polytope 040.645497
hixa tetaope6Dhix atopteta ope, line-first half ofhax0.866025
hixacube6Dhix atop edge-parallelcube0.866025
hixadot6Dhexateron atopdodecateron,hix-first half ofhax0.866025
hixady4Dhecatonicosihexacosidishecatonicosachoron3
hixaf7Dhexateron antifastegium,hix atop invertedhixip,hix-first cap ofnaq0.866025
hixalrix6Dhexateron atop invertedrectified hexateron,hix-firstrotunda ofjak0.816497
hixaltriddip6Dhix atop alternatetriddip, ({3}, perp. {3}, alt.triddip)-trigonic, 1/6-lune ofjak0.816497
hixaope6Dhix atopope, (line, perptet,ope)-trigonic0.866025
hixascad6Dhexateron atopsmall cellated decateron,hix-firstrotunda ofsmall terated tetradecapeton1
hixip6Dhexateron prism,vertex figure ofroc0.816497
hixippy7Dhexateron prism pyramid, vertex-pyramid ofroc0.866025
hixit6Dhexateral (line-)tegum, hexateral dipyramid
hixquathix4Dhecatonicosihexacosaquasitruncated hecatonicosihexacosachoron2.174739
hixquitixhi4Dhecatonicosihexacosiquasitruncated hexacosihecatonicosachoron2.351141
hixquitphix4Dhecatonicosihexacosiquasitruncated prismatohecatonicosihexacosachoron2.483382
hixtaphix4Dhecatonicosihexacositruncated prismatohecatonicosihexacosachoron7.735167
hixthix4Dhecatonicosihexacositruncated hecatonicosihexacosachoron6.186316
hixtixhi4Dhecatonicosihexacositruncated hexacosihecatonicosachoron3.804226
hixu6Dhexateral-based ursapeton ofx3xoo3ooo3ooo3ooo&#xt,hix-basedursulate,vertex figure ofo3o3o3o3o4s3s1.048383
...3Dho oh&#q, narrower variant ofdigonal antiprism1.767767
...3Dho3oh&#q, narrower variant oftrigonal antiprism, hemiation ofhip1.118034
hocoaso4Dhollowcuboctahedron atopstella octangula,tetrahedralcupolaic blend1
hoct5Dhexagon octahedron duoprism1.224745
hoctaoho4Dhollow2oct atopoho1
hocto (alt.: gecdify)8Dhemiocteract, 64(=g)+48(=c)-diminishedfy,Gosset polytope 15,11
hocubasiddo4Dhollowcube atopsnub disoctahedron,icosahedralcupolaic blend1
hocucup4Dhollow cuboid cupoliprism, sixtepeblend, "coord-planes squares star" atop "coord-planes squares star"0.790569
hoddated ex4D(shallow-)hexa-octa-diminished deep-tetra-diminishedhexacosachoron1.618034
hodho4Dhexadecoctidishemioctachoron1
hodidgyt5Dhollowdodecadodecahedralgyrotrigonism1.098185
...5D2didgyrotrigonism1.098185
hodip4Dhexagon - octagon duoprism1.645329
hog dhidicup4Dhollowgidhid cupoliprism0.732444
hog dhidicup verf3Dvertex figure ofhog dhidicup0.730749
hoh honho4Dhexadecoctihemihexadekintercepted hemioctachoron1
hoha3Dhexagonal hemiapeirogonal tesselation
hohoh4Dhexadecoctihemihexadecachoron1
hop (old: hep)6Dheptapeton, 6Dsimplex (α6), pyroex(id),hexateral pyramid,vertex figure ofoca,Gosset polytope 050.654654
hopabril7Dheptapeton atopbirectified heptapeton,hop-first monostratic cap ofhesa0.935414
hopalbril7Dhop atop invertedbril,hop-first cap oflaq1
hopalril7Dhop atop invertedril,hop-first cap ofnaq0.866025
hopastaf7Dhop atopstaf, half ofsuph (itshop-firstrotunda),partial Stott expansion ofoca1
hopip7Dheptapeton prism,vertex figure ofrene0.823754
hopitjak (old: hoptijak)6Ddemiprismatotruncatedicosiheptaheptacontidipeton3.109126
hopu7Dheptapeton-based ursaexon,hop-basedursulate,vertex figure of o3o3o3o3o3o4s3s1.062128
horico adisti5Dhollowrectified icositetrachoron atopdisnub tetrakisicositetrachoron,snub disicositetrachoriccupolaic blend1.738546
hosiap5Dhollow stellated icosatetrachoric antiprism, pseudostico atop pseudostico0.790569
hossdap4Dhollow small stellated dodecahedral antiprism, pseudosissid atop pseudosissid0.707107
...4Dhossdap + 22sissid0.707107
hossidgyt5Dhollowsmall-stellated-dodecahedralgyrotrigonism0.742632
...5D2sissidgyrotrigonism0.742632
hot thibbit4Dhexagonal-omnitruncated-trihexagonal duoprismatic tetracomb
hotet aoho4Dhollow2tet atopoho1
hotetahoct4Dhollowtet atop hollowoct0.774597
hothahacho4Dhollowtetrahemihexahedron atopcubohemioctahedron1
hotjak6Ddemitruncatedicosiheptapeton2.828427
howoh5Dhexadecasphenohexadecateron, cantellatedhexadecahemidecateron1.732051
...4Dvertex figure ofhexadecasphenohexadecateron0.957427
hudsi3Dgreat noble triangular hexecontahedron, dual of H-stellation oficosahedron, H-faceting ofdodecahedron,vertex figure ofpaphacki, huitzilopochtli0.866025
huhoh4Dhexadecahemihexadecachoron1
huht2Dhexahexagonal tiling
...3D(infinite series of) hyperbolic uniform honeycombs withpyritohedral vertex figure

I

ica sidpith, ico || sidpith5Dicositetrachoron atopsmall disprismatotesseractihexadecachoron1.847759
ica tutcup, ico || tutcup5Dicositetrachoron atoptruncated-tetrahedral-cupoliprism1.224745
icaf (alt.: icalicope)6Dicositetrachoron antifastegium,icositetrachoron atop invertedicositetrachoral-prism1.123033
icarico5D(degenerate)ico atoprico∞   i.e. flat in euclidean space
icarit, ico || rit5Dicositetrachoron atoprectified tesseract,ico-first half ofnit1.224745
icarita6Dicositetrachoron atoprectified-tesseractic alterprism, (ico,rit, alt.rit)-trigonic1.290994
icates, ico || tes5Dicositetrachoron atoptesseract1.050501
icathex5Dico atopthex,ico-first segment ofsart1.732051
icau pretasto4Dicositetra-augmentedpentagonorhombic-trisnub-trisoctachoron
icau prissi4Dicositetra-augmented prismatorhombisnub icositetrachoron
ico (alt.: jot)4Dicositetrachoron, 24-cell, xylochoron, octaplex, rectifiedhexadecachoron, birectifiedtesseract, hyperdiamond, joinedtesseract, trisoctachoron,vertex figure ofhext, Voronoi cell oflattice F4, Voronoi cell oflattice D4*, surtegmated tesseract,Gosset polytope 01,1,1,lattice B4 contact polytope (span of its small roots),lattice D4 contact polytope (span of its roots),lattice F4 contact polytope (span of its small roots), equatorial cross-section ofhex-firstrat1
...4Dico+gico+72{4} (?)1
...4Dico+gico+24co (?)1
..., ico || sadi5Dico atopsadi∞   i.e. flat in euclidean space
..., ico || spic5D(degenerate)ico atopspic∞   i.e. flat in euclidean space
..., ico || srit5D(degenerate)ico atopsrit∞   i.e. flat in euclidean space
icoahin6Dico atophin, 1/6-lune ofmo1
icoap (alt.: icoalico)5Dicositetrachoral antiprism,icositetrachoron atop dualicositetrachoron1.050501
icodip8Dicositetrachoron duoprism1.414214
icope5Dicositetrachoron prism1.118034
icopy5D(degenerate)ico pyramid∞   i.e. flat in euclidean space
icot4Dicositetrachoric tetracomb,Voronoi complex of body-centered tesseractic (bct)lattice,Gosset polytope 01,1,1,1
icou5Dicositetrachoron-based ursateron,ico-basedursulate,vertex figure ofs3s4o3o4o3o1.738546
icoy9Dicosayotton, quadrirectified decayotton, equatorial cross-section of (vertex first) 1/q-deker,Gosset polytope 04,41.118034
ictum5D(degenerate)ico-based tutsateron,ico-first bistratic "cap" ofthext∞   i.e. flat in euclidean space
id3Dicosidodecahedron, rectifiedicosahedron, rectifieddodecahedron, equatorial cross-section of vertex-firstex1.618034
...3Did+seihid+sidhid (?)1.618034
...3Dicosidodecahedron faceting1.618034
...4D(0,0,20,0,0)-diminished vertex-first-rotunda of ex, icosi-diminished vertex-first-rotunda ofex, mono-augmented axially-icosahedral ursachoron ofxo3xooo5oooo&#xt1.618034
...4Did -srid - F-ike -ti tower,thawro'drox...
idadope5Dicosidodecahedron atopdodecahedron-prism1.618034
idasrid, id || srid, K-4.1314Dicosidodecahedron atopsmall rhombicosidodecahedron,icosidodecahedron cupola,ike-first supra-cap ofrox3.077684
idasridati4Did atopsrid atopti
idati, id || ti, K-4.1584Dicosidodecahedron atoptruncated icosahedron,icosidodecahedral cap ofsmall rhombated hexacosachoron6.073594
iddei3Dicosidisicosahedron,compound of 5oho1
iddip, K-4.904Dicosidodecahedron prism1.693527
iddoe6Dicosidodecahedron-dodecahedron duoprism2.140458
ided3Dicosidodecadodecahedron1.322876
idhi4Dinvertidodecahedronary hecatonicosachoron1
ididdip4Dicosidodecadodecahedron prism1.414214
idim sidpixhi4Dicosa-diminishedsmall disprismatohexacosihecatonicosachoron5.236068
idimex4Dspid-diminishedex, icosidiminishedex1.618034
idimsrahi4Dicosa-diminishedsmall rhombated hecatonicosachoron6.735034
idimsrix4Dicosa-diminishedsmall rhombated hexacosachoron6.073594
idinaq (alt.: trahixdap)7Dicosa-diminishednaq, triangular-hexatericduoalterprism0.866025
idirek8Dicositetra-diminishedrectified diacosipentacontahexazetton1
idisdid3Dinvertidisnub dodecadodecahedron,compound of 2isdid
idodip6Dicosidodecahedron-icosidodecahedron duoprism2.288246
idprahi4Dicositetra-diminishedprismatorhombated hecatonicosachoron8.278950
idprix4Dicositetra-diminishedprismatorhombated hexacosachoron9.744610
idsid pixhi4Dicositetra-diminishedsmall disprismatohexacosihecatonicosachoron5.236068
idsrahi4Dicositetra-diminishedsmall rhombated hecatonicosachoron6.735034
idsrix4Dicositetra-diminishedsmall rhombated hexacosachoron6.073594
idtid3Dicosidodecatruncated icosidodecahedron, icositruncated dodecadodecahedron2
...3Dhyperbolic honeycomb byidtid andtidect0.485868i
idtiddip4Dicosidodecatruncated-icosidodecahedron prism, icositruncated-dodecadodecahedron prism2.061553
ifbah, ike-6-23D2-fold facetedicosahedron ike-6-2, pentagonal butterfly wedge,blend of 2pentagonal pyramids, half ofblend of 2 pentagonal antiprisms0.951057
ihdlaq7Dicositetra-hexa-diminishedpentacontihexapentacosiheptacontihexaexon,hexadecachoralgyro-cuboctahedronism1
ihi4Dicositetrahemiicositetrachoron1
ikadoaid4D(1,0,0,12,0)-diminished vertex-first-rotunda ofex, trideca-diminished vertex-firstrotunda ofhexacosachoron,ike atop (pseudo)doe atopid1.618034
ikadobcu4Dikadoe bicupola...
...4Dtoroidal (ikadobcu,ipe)-blend...
ikadoe (alt.: ikap), ike || doe, K-4.784Dicosahedron atopdodecahedron,icosahedral antiprism,dodecahedral antiprism, segment of vertex-firsthexacosachoron1.618034
ikaid, ike || id, K-4.1374Dicosahedron atopicosidodecahedron,icosahedral cap ofrectified hexacosachoron,icosahedralcupola3.077684
ike   (alt.: snit)3Dicosahedron, snubtetrahedron, snub tetratetrahedron, snub triangle antiprism, hydrohedron, gyroelongatedpentagonal bipyramid,vertex figure ofex0.951057
...3Dike+3gad (?)0.951057
...4D(1,0,8,12,0)-diminished vertex-first-rotunda of ex, (subsymmetrical) icosiena -diminished vertex-firstrotunda ofhexacosachoron1.618034
..., ike || dope5D(degenerate)ike atopdope∞   i.e. flat in euclidean space
...4D(1,0,4,12,0)-diminished vertex-first-rotunda of ex, heptadeca-diminished vertex-firstrotunda ofhexacosachoron1.618034
ikedip6Dicosahedron-icosahedron duoprism1.344997
ikedoe6Dicosahedron-dodecahedron duoprism1.693527
ikepy, K-4.844Dicosahedral pyramid, vertex cap ofhexacosachoron1.618034
ikhon3Dhyperbolic order 3icosahedral honeycomb0.509376i
ikid6Dicosahedron-icosidodecahedron duoprism1.876844
iktum4Dbistraticicosahedron-first cap oftruncated hexacosachoron,ike-basedtutsatope,ike-based tutism4.643523
iku4D(1,0,20,0,0)-diminished vertex-first-rotunda of ex, (full-symmetrical) icosiena -diminished vertex-first-rotunda ofex, axially-icosahedral ursachoron ofx3xoo5ooo&#xt,ike-basedursulate1.618034
ini4Dicositetrintercepted icositetrachoron1.732051
...4Dinner pentadiminished2/10-luna of ex 1/5-luna ofxfooo5xofxo oxofx5ooxox&#zx
inpac4Dicositetraintercepted prismatotetracontaoctachoron1.847759
...4Dinpac+72{4} (?)1.847759
ipe, K-4.364Dicosahedron prism,vertex figure ofrectified hyperbolic pentachoric honeycomb1.074481
ipixady4Dinvertopental hexacosadishecatonicosachoron3.077684
iquatoc4Dicositetraquasitruncated tetracontoctachoron2
iquatpic4Dicositetraquasitruncated prismatotetracontoctachoron2.828427
iquipadah4Dinverted quasiprismatodishexadecachoron1.485633
irl5Dinvertiretrolepidoteron1.224745
...4Dvertex figure ofinvertiretrolepidoteron0.912871
irohlohn5Dinvertiretrohexadecalepidohemipenteract1.224745
...4Dvertex figure ofinvertiretrohexadecalepidohemipenteract0.912871
isdid3Dinverted snub dodecadodecahedron, vertisnub dodecadodecahedron, nyarlathotep
isdiddip4Dinverted-snub-dodecadodecahedron prism
ite (old: it, older: ikedpy)4D(line-)ikosahedron-tegum, icosahedral bipyramid

J

jak (old: yaz)6Dicosiheptaheptacontidipeton, argyropeton, sideropeton,Gosset polypeton 22,1,vertex figure ofnaq, Delone cell oflattice E6, trifold enneaduoswirlpeton0.816497
jaka (alt.: pabdinaq, old: jakaljak)7Djak alterprism,jak atop invertedjak, vertex-first medial segment ofnaq, parabidiminishednaq0.866025
jakaf (old: jakaljakip)8Dicosiheptaheptacontidipeton alterfastegium,icosiheptaheptacontidipeton atop invertedicosiheptaheptacontidipeton-prism1
jakamo7Djak atopmo,jak-first half of parabidiminishedlaq1
jakap8Djaka prism,jakip alterprism1
jakapy (alt.: pabdinaqpy)8Dicosiheptaheptacontidipetic-alterprism pyramid,parabidimished-hecatonicosihexapentacosiheptacontihexaexon pyramid, (jak, alt.jak, point)-trigonic1
jakarojak7Djak atoprojak,jak-first cap ofranq1.414214
jakatrim7Djak atoptrim,jak-first cap ofstanq1.658312
jakip7Dicosihepta-heptacontidi-peton prism,vertex figure ofriffy0.957427
jakoh6Dicosiheptaheptacontidipetic hexacomb,Gosset hexacomb 22,2,Delone complex oflattice E6
jakoha8Dicosiheptaheptacontidipetic hexacombalterprism∞   i.e. flat in euclidean space
jakpy7Dicosihepta-heptacontidi-peton pyramid, vertex-first cap ofnaq0.866025
jakte7Dicosihepta-heptacontidi-petontegum...
jaku7Djak-based ursaexon1.335149

K

ka10Dchilliaicositetraxennon,decacross (β10), aerodak(id),decayottal antiprism,Gosset polytope 71,1,lattice C10 contact polytope (span of its small roots)0.707107
kadify8Dheptacontadia-diminisheddischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton,tegum sum of two mutually invertedbirectified enneazetta, bidiambooctadecazetton1
kafandoh5Dspikifacetospinodishexadecateron1.620185
...4Dvertex figure ofspikifacetospinodishexadecateron0.951190
kaje6Dheptacontidiaicosiheptapeton,vertex figure ofquil0.816497
katcabadint (alt.: katacbadint)5Dskewtrigonary cellibiprismatodispenteractitriacontaditeron1.5
kavahto4Dskewverted hexadecatrisoctachoron1.414214
kavipathi4Dskewverted prismatotrishecatonicosachoron2.828427
kaviphdit4Dskewverted prismatohexadecadistesseract1.414214
kepisna4Dchiropental snubbachoron, chiralcompound of 6ex inrox army1.618034
kevuthi4Dskewverted tetrishecatonicosachoron2.828427
ki3Dchiro-icosahedron,compound of 5tet0.612372
kidisna4Dchiro-icosahedronary disnubbachoron, chiralcompound of 10ex inrahi army1.618034
kitapna4Dchirotrigonal antiprismattic enenahexachoron, chiralcompound of 4ico inrico army1
kitefa4Dchirotegmic hecatontetracontatetrachoron, chiralcompound of 6ico inspic army1
koho4Dskew octahemioctachoron0.707107
kred (old: red)3Dchiro-rhombidodecahedron,compound of 6pip0.986715
kri3Dchirorhombicosahedron,compound of 10trip0.763763

L

ladbril6Dheptadiminishedbirectified heptapeton0.925820
lanq (inbetween: rolin)7Dpentacontihexa-hecatonicosihexa-pentacosiheptacontihexa-exon, rectified pentacontihexahecatonicosihexaexon,Gosset polytope 03,2,12.449490
lanquoh (old: rolinoh)7Dpentacontihexa-hecatonicosihexa-pentacosiheptacontihexa-exic heptacomb, rectified pentacontihexahecatonicosihexaexic heptacomb,Gosset heptacomb 03,3,1
laq7Dpentacontihexapentacosiheptacontihexaexon, argyroexon,Gosset polyexon 21,3,vertex figure ofnaquoh,lattice E7 contact polytope (span of its roots), equatorial cross-section of vertex-firstfy1
laqalin8Dpentacontihexapentacosiheptacontihexaexon atoppentacontihexahecatonicosihexaexon,21,3 atop12,3,laq-first cap ofbay,21,3-first cap of21,41.414214
laqpe8Dpentacontihexapentacosiheptacontihexaexon prism1.118034
lawx5Dlepidosphenary hexateron1.290994
...4Dvertex figure oflepidosphenary hexateron0.921954
lifpipixhi4Dpolar facetopental prismatohexacosahecatonicosachoron3.077684
lin7Dpentacontihexahecatonicosihexaexon, chrysoexon,Gosset polyexon 12,3, Voronoi cell oflattice E7*1.322876
linaranq8Dpentacontihexahecatonicosihexaexon atoprectified pentacontihexapentacosiheptacontihexaexon,laq-first subsegment ofbay1.414214
linoh7Dpentacontihexahecatonicosihexaexic heptacomb,Gosset heptacomb 13,3,Voronoi complex oflattice E7*
...3Dlamina-truncate of hyperbolico8o4x *b3x tesselation0.321797i
...4Dlamina-truncate of hyperbolicx3x4x338o tesselation1.864101i
...3Dlamina-truncate of hyperbolicx4x3o8o tesselation0.594604i

M

...3Ddual of uniformtriangular prism, triangular dipyramid (butnottridpy),o3m3o3o cell
...3Ddual ofhexagonal prism, hexgonal dipyramid
...3Ddual of uniformn-gonal prism, n-gonal dipyramid
...4Dgreat-rhombated-pentachoron dual
...4Dsmall-rhombated-pentachoron dual
mabaud, J603Dmetabiaugmented dodecahedron
mabauhip, J563Dmetabiaugmented hexagonal prism
mabautid, J703Dmetabiaugmented truncated dodecahedron
mabgyrid, J743Dmetabigyrated rhombicosidodecahedron2.232951
mabidrid, J813Dmetabidiminished rhombicosidodecahedron2.232951
mabirch3Dmedial birhombatocubic honeycomb
mabred4Dmedial birhombatodecachoronsqrt[(2a2+2ab+3b2)/5]
mabric4Dmedial birhombatotetracontoctachoronsqrt[a2 + 2 sqrt(2) ab + 3b2]
madek6Dpentacontatetradisheptacontadipeton,compound of 2jak0.816497
magydrid, J783Dmetagyrate diminished rhombicosidodecahedron2.232951
mardatathi4Dmedial retroditetrahedral triakishecatonicosachoron1.414214
...4Dmaximally expandedWitting polychoron,complex polychoronx3-3-o3-3-o3-3-x3
...4Dmaximally expandedgeneralized Shephard tesseract,complex polychoronxp-4-o2-3-o2-3-x2
medrojak (alt.: tritith)6Dpentacontitetra-diminishedrojak, tri -(triangle,triangle,hexagon)-trioprism1.290994
mesdi4Dmedial snub disicositetrachoron1
mesdi-verf3Dvertex figure ofmedial snub disicositetrachoron0.866025
mibdi, J623Dmetabidiminished icosahedron0.951057
mibdiadoe, mibdi || doe, K-4.824Dmetabidiminished icosahedron atopdodecahedron, metabidiminished segment of vertex-firsthexacosachoron1.618034
mibdinit5Dmetabidiminishednit, rectifiedbidhin1.224745
mibdip4Dmetabidiminished-icosahedron prism1.074481
mibdipy, K-4.874Dmetabidiminished-icosahedral pyramid1.618034
mibdirit4Dmetabidiminishedrectified tesseract, wedge-diminishedrectified tesseract, bistraticcuboctahedron based wedge1.224745
mibkid3Dmetabikisdodecahedron, (subsymmetrically) metabistellated-dodecahedron, dual ofmibdi
middit thix4Dmedial ditrigonal trishecatonicosihexacosachoron1.732051
mif pixady4Dcircumfacetopental hexacosadishecatonicosachoron0.726543
mipthi4Dmedial prismatotriakishecatonicosachoron3.199386
mix4Dmedial hexacosachoron, mete-star,compound of 120pen0.632456
mo6Dpentacontitetrapeton, chrysopeton,Gosset polypeton 12,2,vertex figure ofjakoh,lattice E6 contact polytope (span of its roots), equatorial cross-section ofjak-firstlaq1
moarojak7Dmo-first monostratic cap oflin,mo atoprojak1.322876
mohiny4Dmedial hecatonicosintercepted hecatonicosachoron1.070466
...3Dmono lowered small rhombicuboctahedron...
...3Dmono lowered truncated cube...
mort3Dmedial rhombic triacontahedron
mou7Dmo-based ursaexon1.738546
mrawv hixhi4Dmedial retrosphenoverted hecatonicosihexacosihecatonicosachoron3.963358
mriphi4Dmedial retropental hecatonicosachoron1.902113

N

n,co-dip5Dn-gon - cuboctahedron duoprismsqrt[1+1/(4 sin2(π/n))]
n,co-dippip6Dn-gon - cuboctahedron duoprismatic prism
n,cube-dip5Dn-gon - cube duoprismsqrt[3/4+1/(4 sin2(π/n))]
n,doe-dip5Dn-gon - dodecahedron duoprismsqrt[(9+3 sqrt(5))/8+1/(4 sin2(π/n))]
n,doe-dippip6Dn-gon - dodecahedron duoprismatic prism
n,ex-dip6Dn-gon - hexacosachoron duoprism
n,girco-dip5Dn-gon - great-rhombicuboctahedron duoprismsqrt[(13+6 sqrt(2))/4+1/(4 sin2(π/n))]
n,grid-dip5Dn-gon - great-rhombicosidodecahedron duoprismsqrt[(31+12 sqrt(5))/4+1/(4 sin2(π/n))]
n,hex-dip6Dn-gon - hexadecachoron duoprismsqrt[2+1/sin2(π/n)]
n,hi-dip6Dn-gon - hecatonicosachoron duoprism
n,hix-dip7Dn-gon - hexateron duoprismsqrt[5/12 + 1/(2 sin(π/n))2]
n,ico-dip6Dn-gon -icositetrachoron duoprism
n,id-dip5Dn-gon - icosidodecahedron duoprismsqrt[(3+sqrt(5))/2+1/(4 sin2(π/n))]
n,id-dippip6Dn-gon - icosidodecahedron duoprismatic prism
n,ike-dip5Dn-gon - icosahedron duoprismsqrt[(5+sqrt(5))/8+1/(4 sin2(π/n))]
n,ike-dippip6Dn-gon - icosahedron duoprismatic prism
n,m,k-tip6Dn-gon - m-gon - k-gon - triprismsqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/k))]
n,m,k-tippip7Dn-gon - m-gon - m-gon - triprismatic prismsqrt[1/4+1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/m))]
n,m,p,q-quip8Dn-gon - m-gon - p-gon - q-gon - tetraprism (or: -quadprism)sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/p))+1/(4 sin2(π/q))]
n,m-dafup5D(n,m)-duoantifastegiaprism, (n,m)-duoantiwedge,(n,m)-dip atop bidual(n,m)-dipsqrt([2+1/(1-cos(π/n))+1/(1-cos(π/m))]/8)
n,m-dap4Dn-gon - m-gon duoantiprism, hemiated 2n-gon - 2m-gon duoprismsqrt[A2/(4 sin2(π/2n))+B2/(4 sin2(π/2m))]
n,m-dip4Dn-gon - m-gon duoprismsqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))]
n,m-dippip5Dn-gon - m-gon duoprismatic prismsqrt[1/4+1/(4 sin2(π/n))+1/(4 sin2(π/m))]
n,n,k-tip6Dn-gon - n-gon - k-gon - triprismsqrt[1/(2 sin2(π/n))+1/(4 sin2(π/k))]
n,n,n,n-quip8Dn-gon - n-gon - n-gon - n-gon - tetraprism (or: -quadprism)sqrt[1/sin2(π/n)]
n,n,n-tip6Dn-gon - n-gon - n-gon - triprismsqrt[3/(4 sin2(π/n))]
n,n,n-tippip7Dn-gon - n-gon - n-gon - triprismatic prismsqrt[1/4+3/(4 sin2(π/n))]
n,n-dip4Dn-gon - n-gon duoprism1/(sqrt(2) sin(π/n))
n,n-dippip5Dn-gon - n-gon duoprismatic prismsqrt[1/4+1/(2 sin2(π/n))]
n,oct-dip5Dn-gon - octahedron duoprismsqrt[1/2+1/(4 sin2(π/n))]
n,oct-dippip6Dn-gon - octahedron duoprismatic prism
N,pen-dip6DN-gon - pentachoron duoprismsqrt[1/(4 sin2(π/N))+2/5]
n,rahi-dip6Dn-gon - rectified-hecatonicosachoron duoprism
n,rap-dip6Dn-gon - rectified-pentachoron duoprism
n,rico-dip6Dn-gon - rectified-icositetrachoron duoprism
n,rit-dip6Dn-gon - rectified-tesseract duoprism
n,rox-dip6Dn-gon - rectified-hexacosachoron duoprism
n,sirco-dip5Dn-gon small-rhombicuboctahedron duoprismsqrt[(5+2 sqrt(2))/4+1/(4 sin2(π/n))]
n,srid-dip5Dn-gon - small-rhombicosidodecahedron duoprismsqrt[sqrt(5)+11/4+1/(4 sin2(π/n))]
n,tes-dip6Dn-gon - tesseract duoprism
n,tet-dip5Dn-gon - tetrahedron duoprism, n-gonal duofastegium,n-gonal prismdisphenoidsqrt[3/8+1/(4 sin2(π/n))]
n,tet-dippip6Dn-gon - tetrahedron duoprismatic prism
n,ti-dip5Dn-gon - truncated-icosahedron duoprismsqrt[(29+9 sqrt(5))/8+1/(4 sin2(π/n))]
n,tic-dip5Dn-gon - truncated-cube duoprismsqrt[sqrt(2)+7/4+1/(4 sin2(π/n))]
n,tid-dip5Dn-gon - truncated-dodecahedron duoprismsqrt[(37+15 sqrt(5))/8+1/(4 sin2(π/n))]
n,toe-dip5Dn-gon truncated-octahedron duoprismsqrt[5/2+1/(4 sin2(π/n))]
n,tut-dip5Dn-gon - truncated-tetrahedron duoprismsqrt[11/8+1/(4 sin2(π/n))]
n-af, K-4.1744Dn-gonal antifastegium, n-gonal -n-antiprismatic wedge, {n} || gyron-prismsqrt[(1+2 cos(π/n)-2 cos2(π/n))/(2+4 cos(π/n)-6 cos2(π/n))]
n-ap3Dn-gonal antiprismsqrt[(3-2 cos(π/n))/(8-8 cos(π/n))]
n-appip, K-4.1764Dn-antiprism prismsqrt[(5-4 cos(π/n))/(8-8 cos(π/n))]
n-appy4Dn-antiprismatical pyramidsqrt[(2-2 cos(π/n))/(5-6 cos(π/n))]
n-apt4D(line-)n-antiprismatic tegum,n-antiprismatic bipyramid,n-pyramidal antiprism
n-aw, {2n} || n-ap4Danti-n-wedge, n-gonal anti-wedge, 2n-gon -n-antiprismatic wedge, n-gonal gyrobicupolaic ring, {2n} ||n-antiprism, {n} || gyratedn-cupolasqrt[(3-2 cos(π/n))/(5-6 cos(π/n))]
n-azedip3Dn-gonal - apeirogonal duoprism
...4Dn-fold dissectedcubic polytwister, n-fold dissected cubiter,cubiswirlic 6n-choron...
n-cuf4Dn-gonal cupofastegium, 2n-gon -n-prismatic wedge, n-gonal orthobicupolaic ring, {2n} ||n-prism, {n} ||n-cupolasqrt[(5+2 cos(π/n)-4cos2(π/n))/(8-12 cos2(π/n))]
n-cufbil4Dn-gonal cupofastegia biluna
n-dep4Dn-gonal duoexpandoprism, expandedn-n-duoprism,tegum sum of 2 alternatedn-2n-duoprismssqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/n))]
...4Dn-fold dissecteddodecahedron polytwister, n-fold dissected doter,dodecaswirlic 12n-choron...
...6D(N-g, dual N-g, paraN-p, gyroN-p)lace simplex...
..., N-g || N-appip5DN-gon atopN-appip, (N-gon, N-p, gyro N-p)-trigonic...
...4Dn-fold dissectedgreat-dodecahedral polytwister, n-fold dissected gaditer,great-dodecaswirlic 12n-choron...
n-gytpuf4Dn-gonal gyrotegmicupolafastegium,n-cupola atop inverted gyratedn-cupola,2n-prismatic gyrated bi-wedge
...4Dn-fold dissectedicosahedral polytwister, n-fold dissected ikter,icosaswirlic 20n-choron...
...4D(n,m)-double antiprismatoid...
n-m-det4D(n,m)-ditetragoltriate...
..., N,M-dip || N,M-dafup6D(N,M)-duoprism atop(N,M)-duoantifastegiaprism, ((N,M)-dip, (N,dual M)-dip, (dual N,M)-dip)-trigonic...
...4Dn-fold dissectedoctahedral polytwister, n-fold dissected octer,octaswirlic 8n-choron...
n-p3Dn-gonal prismsqrt[1/4+1/(4 sin2(π/n))]
n-pidpy4Dn-prismatic bipyramid
n-pipy4Dn-prism pyramid, general vertex pyramid of o-3-x-3-o-n-o1/sqrt[3 - 1/sin2(π/n)]
n-puf4Dn-gonal pucofastegium, n-gon -2n-prismatic wedge, n-gonal magnabicupolaic ring, {n} ||2n-prism, {2n} ||n-cupolasqrt[(2 cos2(π/n)-2 cos(π/n)-3)/(6 cos2(π/n)-2)]
n-sc, n-pyr-pyr4D{n}-scalene, {n}-pyramidal pyramid, ntet rosette, line atop fully orthogonal {n}sqrt[(4 sin2(π/n)-1)/(3 sin2(π/n)-1)]/2
n-tepuf4Dn-gonal tegmipucofastegium,n-cupola atop inverted orthon-cupola,2n-prismatic ortho bi-wedge
...4Dn-fold dissectedtetrahedral polytwister, n-fold dissected tetter,tetraswirlic 4n-choron...
n/2-ap3Dn/2 antiprismsqrt[(3-2 cos(2π/n))/(8-8 cos(2π/n))]
n/d,2n/d-dip4Dn/d-gram - 2n/d-gram duoprismsqrt[1/(4 sin2(π d/n))+1/(4 sin2(π d/2n))]
n/d,2n/d-dipcup5Dn/d,2n/d-dip cupoliprismsqrt([7+4 cos(π d/n)-2 cos2(π d/n)]/[8-8 cos2(π d/n)])
n/d,m/b-dip4Dn/d-gram - m/b-gram duoprismsqrt[1/(4 sin2(π d/n))+1/(4 sin2(π b/m))]
n/d-af4Dn/d-grammal antifastegium, n/d-grammal -n/d-antiprismatic wedge, {n/d} || gyron/d-prismsqrt[(1+2 cos(π d/n)-2 cos2(π d/n))/(2+4 cos(π d/n)-6 cos2(π d/n))]
n/d-ap3Dn/d-antiprism, n-antiprism with winding number d (for d>n/2 also: n/(n-d)-retroprism, retrograde n/(n-d)-antiprism)sqrt[(3-2 cos(π d/n))/(8-8 cos(π d/n))]
n/d-appip4Dn/d-antiprism prismsqrt[(5-4 cos(π d/n))/(8-8 cos(π d/n))]
n/d-cu3Dn/d-gonal cupolasqrt[(7+4 cos(π d/n)-4 cos2(π d/n))/(12-16 cos2(π d/n))]
n/d-cuf4Dn/d-grammal cupofastegium, 2n-gon -n/d-prismatic wedge, n/d-grammal orthobicupolaic ring, {2n/d} ||n/d-prism, {n/d} ||n/d-cupolasqrt[(5+2 cos(π d/n)-4cos2(π d/n))/(8-12 cos2(π d/n))]
n/d-cupe4Dn/d-cupola prism,n/d-prism atop2n/d-prismsqrt[(5+2 cos(π d/n)-4 cos2(π d/n))/(6-8 cos2(π d/n))]
n/d-daf5Dn/d-duoantifastegium, (2,n)-duoantiwedge,n/d-p atop bidualn/d-psqrt([3+1/(1-cos(pi d/n))]/8)
n/d-dow5Dn/d-grammal disphenoid, n/d-grammal biwedge, n/d-grammal duopyramid, {n/d} || perp {n/d}sqrt[1+1/(2 sin2(π d/n))]/2
n/d-p3Dn/d-prism, n-prism with winding number dsqrt[1/4+1/(4 sin2(π d/n))]
n/d-py3Dn/d-gonal pyramid1/sqrt[4-1/sin2(πd/n)]
n/d-pyp4Dn/d-pyramidal prism, line ||n/d-prismsqrt[1/4+1/(4-1/sin2[π d/n])]
...5D{N} atop gyrated3,N-dip, (N-g, dual N-g, N-p)-trigonic...
nal7Dhecatonicosihexa-pentacontihexa-exon,vertex figure offib0.866025
naq (alt: rocalroc)7Dhecatonicosihexapentacosiheptacontihexaexon, sideroexon,Gosset polyexon 32,1, alterelongatedjaktegum,vertex figure offy, (one of the) Delone cell(s) oflattice E7,tegum sum of 2 mutually invertedrectified octaexa, biambohexadecaexon,lattice E7* contact polytope (span of its roots)0.866025
naqalaq8Dnaq atoplaq, second stratos of vertex-firstfy, E7 1/2 polytope1
naqpe8Dnaq prism, prism ofGosset polyexon32,1,vertex figure ofrigoh1
naqpy8Dhecatonicosihexapentacosiheptacontihexaexon pyramid, vertex-first cap offy1
naqu8Dnaq-based ursazetton1.432173
naquiptant5Dpenteractiquasiprismatotruncated penteractitriacontaditeron1.621320
naquitant5Dpenteractiquasitruncated penteractitriacontaditeron1.354911
naquoh7Dhecatonicosihexapentacosiheptacontihexaexic heptacomb,Gosset heptacomb 33,1,Delone complex oflattice E7
narptint5Dpenteractiretroprismatotruncated penteractitriacontaditeron2.621320
nat5Dspinotriacontaditeron1.224745
...4Dvertex figure ofspinotriacontaditeron0.912871
nav9Denneractipentacosidodecayotton1.581139
...4Dn/d-grammic retroantiprismatic hemiantiprism0.707107
nibdihin5Dneighbourly bidiminishedhemipenteract0.790569
nipdip4Dspinoprismatodispentachoron1
nipixady4Dintercepted invertopental hexacosadishecatonicosachoron3.077684
nippant5Dpenteractiprismated penteractitriacontaditeron3.505073
niptant5Dpenteractiprismatotruncated penteractitriacontaditeron2.621320
nit5Dpenteractitriacontiditeron, birectifiedpenteract, birectifiedtriacontiditeron, birectified pentacross,Gosset polytope 02,1,1, equatorial cross-section ofrat-firstbrag1.224745
nitarin6Dnit atoprin,nit-firstrotunda ofbrox1.414214
nitasiphin6Dnit atopsiphin,hin-first medial segment ofrojak1.290994
nitasirhin6Dnit atopsirhin,nit-first cap ofram1.732051
nitip6Dpenteractitriacontiditeron prism1.322876
...3Dnoble {9,3} modwrap withinsrid, Crennell number 4 stellation of the icosahedron2.232951
nophap5Dspinopentachoric hemiantiprism, pseudo pentachoric hemiantiprism0.707107
noqrant5Dpenteractiquasirhombated penteractitriacontaditeron1.849749
noqraptant5Dpenteractiquasiretroprismatotruncated penteractitriacontaditeron1.621320
noquapant5Dpenteractiquasiprismated penteractitriacontaditeron2.283521
nottant5Dpenteractitruncated penteractitriacontaditeron2.159679
nurrant5Dpenteractirhombated penteractitriacontaditeron3.013043

O

...4Domni-pecu-augmented (10,10)-duoprism
...4Domni-pecu-augmented (10,20)-duoprism
...4Domni-pippy-augmented (5,10)-duoprism
...4Domni-pippy-augmented (5,20)-duoprism
...4Domni-pecu-gyroaugmented (10,10)-duoprism
...4Domni-pecu-gyroaugmented (10,20)-duoprism
...6DhyperbolicGosset pentacomb 01,1,1,1,1,10.707107i
...6Dbidodecateric heptacontadipeton,pentacontitetrapeton dual, convex hull ofmadek0.816497
...5Dhyperbolic order 3 icositetrachoric-tetracomb pentacomb, hyperbolicGosset pentacomb 01,1,1,1,11i
...5Dhyperbolic o3o3o3o4s3s pentacomb2.058171i
...5Dhyperbolic truncatedorder 3 icositetrachoric-tetracomb pentacomb3.316625i
...4Dhyperbolic o3o3o3o *b3x3*c tesselation0.5i
...3Dhyperbolic o3o3o4s4*a tesselation
...3Dhyperbolic o3o3o4s4*b tesselation0.267261i
...3Dhyperbolic o3o3o4x4*a tesselation0.5i
...3Dhyperbolic o3o3o4x4*b tesselation0.377964i
...4Do3o3q4x, variation oftat2.645751
...4Do3o3β4o (?)...
...4Do3o3β4x (?)...
...4Do3o3β5o (?)...
...4Do3o3β5x (?)...
...4Dhyperbolic(order 3) cubic-honeycomb-tetracomb snub...
...3Dhyperbolic o3o4o5x tesselation0.509376i
...3Dhyperbolic o3o4o8x tesselation0.400236i
...3Dhyperbolic o3o4s4o4*a tesselation
...3Dhyperbolic o3o4x4o4*a tesselation0.292893i
...3Dhyperbolic o3o4x4o4*b tesselation0.216606i
...2Dhyperbolic tetrapentagonal tiling of family o3o4o5*a0.438176i
...3Dhyperbolic o3o5o10x tesselation0.202376i
...3Dhyperbolic o3o5o5x tesselation0.245719i
...3Dhyperbolic o3o5x5o5*b tesselation
...4Do3q3o4x, variation ofsrit2.236068
...3Do3q4x, variation oftruncated cube2.179449
...4Do3β3o4β (?)...
...4Do3β3o5β (?)...
...4Do3β3β3o (?)...
...4Do3β3β4o (?)...
...4Do3β3β4β (?)...
...4Do3β3β5o (?)...
...4Do3β3β5β (?)...
...4Do3β3x3o (?)...
...4Do3β3x4o (?)...
...4Do3β3x4β (?)...
...4Do3β3x4x (?)...
...4Do3β3x5o (?)...
...4Do3β3x5β (?)...
...4Do3β3x5x (?)...
...3Do3β4o (?)1
...4Do3β4o3o (?)...
...4Do3β4β3o (?)...
...3Dhyperbolic o3β4β3o5*a tesselation
...3Do3β4x (?)1.778824
...4Do3β4x3o (?)...
...3DHolosnub icosidodecahedron1.618034
...3Do3β5x (?)2.969449
...4Dhyperbolic o3x3o3o *b3o3*c tesselation0.632456i
...4Do3x3β4o (?)...
...4Do3x3β5o (?)...
...3Dhyperbolic cyclotruncated tetrahedral-icosahedral honeycomb0.786151i
...3Dhyperbolic o3x3x4o4*b tesselation0.886405i
...3Dhyperbolic o3x3x4x4*b tesselation1.428194i
...3Dhyperbolic honeycomb o3x4o4o5/2*b0.485868i
...2Dhyperbolic tritetragonal tiling of family o3o4o5*a0.297397i
...3Dhyperbolic o3x4o6o tesselation0.447214i
...3Do3x4q, variation oftruncated cube, hull ofsno2.121320
...3Do3x4u, variation oftruncated cube2.613126
...3Dhyperbolic o3x4x3o5*a tesselation, cyclotruncated cubic-icosahedral honeycomb
...4Dhyperbolic o3x4x3o8o tesselation0.594604i
...2Dhyperbolic ditetragonal tiling of family o3o4o5*a0.921730i
...3Dhyperbolic o3x5x3o5*a tesselation
...3Dhyperbolic o3xØx3*a3xØx3*a tesselation
...3Dhyperbolic o3x:s3s4s honeycomb, hyperbolic rectifiedx3o:s3s4s honeycomb...i
...3Dhyperbolic o3x:s3s5s honeycomb, hyperbolic rectifiedx3o:s3s5s honeycomb...i
...3Dhyperbolic o3x:s3s6s honeycomb, hyperbolic rectifiedx3o:s3s6s honeycomb...i
...3Dhyperbolic o3x:s3sPs honeycomb, hyperbolic rectifiedx3o:s3sPs honeycomb...i
...3Dhyperbolic o4o3x3x3*b tesselation1i
...4Dhyperbolic o4s4o3*a4s4o3*a tetracomb0.25i
...3Dfamily of (generally hypercompact) hyperbolic o4s4o2Qo honeycombs (Q≥2)
...3Dfamily of hyperbolic o4s4oPo honeycombs (P≠2)
...3Do4x3o5β (?)...
...4Dhyperbolic o4x4o3*a4x4o3*a tetracomb0.353553i
...3Dfamily of (generally hypercompact) hyperbolic o4x4o2Qo honeycombs (Q≥2)
o4x4oP*a2Dfamily of (generally hyperbolic) order 2P square tilings
...3Dfamily of hyperbolic o4x4oPo honeycombs (P≠2)
...3Dhyperbolic o4x6o4o tesselation0.5i
...3Do5/2f5x variation oftruncated great dodecahedron2.478019
...3Do5/2β5o (?)1
...3Do5/2β5x (?)...
...4Dhyperbolic birectified order 5 hecatonicosachoric tetracomb0.747674i
...3Dhyperbolic holosnubbed disdodecahedral honeycomb, hyperbolic o5β3β5o honeycomb
...3Dhyperbolic o5x3o3o5/2*b tesselation, rectifiedditdih0.882265i
...3Do5x3o5β (?)...
...3Dhyperbolic o6o4x3xØo3*c tesselation0.447214i
...3Dhyperbolic honeycomb o6o5x∞xØx∞*c *b3*e0.363271i
...3Dhyperbolic honeycomb o6o5x∞x3*b0.363271i
...3Dhyperbolic o8o3x *b4xØx tesselation0.321797i
...3Dhyperbolic o8o4x *b3x tesselation0.321797i
...3Dhyperbolic o8o4x *b3xØx3*b tesselation0.321797i
...4Dicositetrachoron-derived Gévay polychoron, rectifiedo3m4o3o...
...4Dtesseract-derived Gévay polychoron, rectifiedo4m3o3o...
...4Dhecatonicosachoron-derived Gévay polychoron, rectifiedo5m3o3o...
oaf, K-4.584Doctagonal antifastegium, octagon -oap wedge, {8} || gyroop1.409438
oap, 8-ap3Doctagonal antiprism1.375549
oappip, K-4.654Doctagonal-antiprism prism1.463603
...3D(hi derived) truncatedtridpy variant,o2o3o symmetricco relative...
...3D(ico derived) truncatedtridpy variant,o2o3o symmetricco relative...
...3D(tes derived) truncatedtridpy variant,o2o3o symmetricco relative...
oca (old: oc)7Doctaexon, 7Dsimplex (α7), pyrozett(id),heptapetal pyramid,vertex figure ofene, (one of the) Delone cell(s) oflattice E7,Gosset polytope 060.661438
ocalroc8Doca atop invertedroc,oca-first cap offy1
ocat2Dhyperbolic order 3 octagonal tiling1.345608i
oco (old: occo)5Doctagon cuboctahedron duoprism1.645329
ococat2Dhyperbolic order 8 octagonal tiling0.227545i
ocpe8Doctaexon prism,vertex figure ofreday0.829156
oct (alt.: trap, tatet)3Doctahedron, rectifiedtetrahedron,tricross (β3), tetratetrahedron, aerochor(id), trigonalantiprism, snubbed triangular dihedron, larger Delone cell of face-centered cubic (fcc)lattice, equatorial cross-section of (vertex first) 1/q-tes,vertex figure ofhex,Gosset polytope 01,1,lattice C3 contact polytope (span of its small roots), equatorial cross-section of vertex-firsthex0.707107
...3Dinternalcompound ofoctahedron with 4 gyratedtetrahedra
...3Doct+6{4} (?)0.707107
...5Drap atoptetaco, 0.352416-lune ofrat,oct-firstlune ofrat, (tet,oct,tet,co)-cyclelace ring1
...4Daugmented axially-tetrahedral ursachoron ofxo3xooo3oooo&#xt...
..., oct || perp oct7D(degenerate) oct atop fully orthogonal oct, octahedron disphenoid∞   i.e. flat in euclidean space
...4DoxFxofx3xooxFxo3ofxfooo&#xt   (F=ff=x+f)
...4DoxFxoo3xooxFx3ofxfox&#xt   (F=ff=x+f)
...4DoxFxofx3xfoxFxo3ooxfooo&#xt   (F=ff=x+f)
...4DoxFxoo3xfoxFx3ooxfox&#xt   (F=ff=x+f)
octa tethex8Doct atoptethex1
octa tratet6Doct atoptratet,oct-first cap ofril0.845154
octa tutcup, oct || tutcup5Doct atoptuta1.274755
octacho4Doctahedron atopcubohemioctahedron1
octaco, K-4.294Doctahedron atopcuboctahedron, half oficositetrachoron (itsoct-firstrotunda), rectifiedoctahedron-pyramid1
octacope5Doct atopcope,oct-first cap ofnit1.224745
octacube (alt.: octap), oct || cube, K-4.154Doctahedron atopcube,octahedral antiprism,cubical antiprism,vertex figure oficoap0.879465
octasc5Doctahedralscalene,octahedron-pyramid pyramid, line atop fully orthogonaloctahedron, 1/4-lune oftriacontiditeron0.707107
octasirco, oct || sirco, K-4.1074Doctahedron atopsmall rhombicuboctahedron,octahedral cap ofsmall prismatotetracontoctachoron1.847759
octasircoacube4Doct atopsirco atopcube
octatepe (alt.: tettet octtric)5Doct atoptepe, diminishedrix, (tet,tet,oct)-trigonic0.816497
octatepepy6Doctatepe pyramid, (point,tet,tet,oct)lace simplex0.866025
octatetdip7Doct atoptetdip,oct-first half ofroc0.866025
octatoe, oct || toe4D(degenerate)octahedron atoptruncated octahedron∞   i.e. flat in euclidean space
octatricu, oct || tricu, K-4.304Doctahedron atoptrigonal cupola, 2/6-luna oficositetrachoron1
octatut, oct || tut, K-4.524Doctahedron atoptruncated tetrahedron,octahedral cap ofsmall rhombated pentachoron1.183216
...4Doctatut,tricuf-blend
octatutbicu4Doctatut bicupola...
octatuttip (alt.: octtut tuttric)5Doct atoptuttip, (oct,tut,tut)-trigonic1.414214
octco6Doctahedron-cuboctahedron duoprism1.224745
octco tuttric5D(oct,co,tut)-trigonic1.224745
octcube6Doctahedron-cube duoprism1.118034
octdip6Doctahedron-octahedron duoprism, dual of Delone cell oflattice D6*,vertex figure oftraxh1
octdoe6Doctahedron-dodecahedron duoprism1.569562
octepe7Doctahedralpennene0.707107
octet3Dalternated cubic honeycomb, tetrahedral-octahedral honeycomb,Delone complex of face-centered cubic (fcc)lattice
...3Dalternated cubically truncatedrhombic dodecahedral honeycomb
octete6Doctahedraltettene,octahedral-pyramid pyramid pyramid, triangle atop fully orthogonaloctahedron0.707107
octh3Dhyperbolic order 4octahedral honeycomb0i
octhex7Doctahedron - hexadecachoron duoprism,vertex figure of troch1
octhipdaw (alt.: traporhip)5D(oct,hip)-disphenoid, (oct,hip)-duopyramid,trigonal antiprism atop axis-orthogonalhexagonal prism1.224745
octhix8D(octahedron,hexateron)-duoprism,vertex figure oftarn0.957427
octico7Doctahedron - icositetrachoron duoprism1.224745
octid6Doctahedron-icosidodecahedron duoprism1.765796
octike6Doctahedron-icosahedron duoprism1.185120
octo8Docteract, hexadecazetton, 8Dmeasure-polytope (γ8), geoyott(id)1.414214
octpen7Doctahedron - pentachoron duoprism,vertex figure oftro0.948683
octpy || octaco5Dvertex-first 1/4-lune ofrectified triacontiditeron,octahedron-pyramid atopocthedron-first-rotunda-of-icositetrachoron1
octpy, K-4.34Doctahedral pyramid, half ofhex (its vertex-firstrotunda)0.707107
octpyp, line||ope5Doctahedron-prismatic wedge, line atopope,octahedral-pyramid prism, half ofhexip0.866025
octrap7Doctahedron - rectified-pentachoron duoprism1.048809
octsnich4Dhyperbolicoctahedral -snub-cubic honeycomb0.380999i
octu4Daxially-octahedral ursachoron ofx3xoo4ooo&#xt,oct-basedursulate,vertex figure ofs3s4o3o4o1.144123
octum4Doctahedron-firstrotunda oftruncated hexadecachoron,oct-basedtutsatope,oct-based tutism1.581139
ocube5Doctagon - cube duoprism1.567516
...3DWaterman polyhedron number 9 wrt. face-centered cubiclattice A3 centered at a lattice point3
oddimo (alt.: bittip)6Doctadeca-diminishedmo, bitriangular trioprism, triangular trioalterprism1
odedip4Doctagon-decagon duoprism2.079697
odhax6Doctadiminishedhemihexeract0.866025
odho4Doctidishemioctachoron1
...4Docta-diminishedthawro-wedged 2/6-luna ofhexacosachoron...
odinaq (alt.: hexgyo)7Docta-diminishednaq,hexadecachoralgyro-octahedronism0.866025
odip4Doctagon-octagon duoprism1.847759
odipt4Doctagonal-duoprismatic tetracomb0.321797i
oditico4Doctadiminishedtruncated icositetrachoron,Waterman polychoron number 4 wrt. alternated tessiclattice D4 centered at a hole2.645751
odnit5Doctadiminishedpenteractitriacontiditeron1.224745
odoe5Doctagon - dodecahedron duoprism1.915889
odsnic3Doctadiminishedsnub cube, chiral 4folddodecahedron-like barrel,vertex figure ofoctsnich1.343713
...4DoFfoo3ooxxF3Fxoxo3ooffx&#zx
...4DoFFxx3xxoof3fooxo3ooffx&#zx
...4DoFFxx3xxoof3fooxx3xxFFo&#zx
...4DoFFxx3xxoxf3Fxxox3oofFx&#zx
ofiddady4Domnifacetododecahedronary dishecatonicosachoron1
...4DofoxFxo3xxFxoox3xoofxfo&#xt   (F=ff=x+f)
ofpipixhi4Domnifacetopental prismatohexacosahecatonicosachoron0.726543
...3D4foldteddi analog1.144123
...4DoFxFox5AxFoFx2oxofox5ooxofx&#zx
...4DoFxx3xxof3foxo3oofx&#zx
...4Daxially pyritohedral octa-diminishing oftelex, hexa-diminishing ofoofoo3oxoxo5xooox&#xt
...4DoFxxox5Fofxfo oxofox5ooxofx&#zx
...4DoFxxx5Fofxo oxofx5ooxox&#zx
ogasc4Doctagram-scalene, octagram-pyramidal pyramid, line atop fully orthogonal octagram0.621876
ogdow5Doctagrammic disphenoid, octagrammic duopyramid, octagram atop fully orthogonal octagram0.629640
ogirco5Doctagon - great-rhombicuboctahedron duoprism2.660531
ogpy, 8/3-pyr3Doctagrammic pyramid0.594604
ogquithdow6D(octagram,quith)-disphenoid, (octagram,quith)-duopyramid, octagram atop fully orthogonalquasitruncated hexahedron0.639069
ogrid5Doctagon - great-rhombicosidodecahedron duoprism4.020611
oh4Doctahemihexadecachoron1
ohix7Doctagon -hexateron duoprism1.457317
oho3Doctahemioctahedron, facetorectified cube, allelotetratetrahedron1
...3Doho+8{3}1
ohoa hotut4Doho atop hollow2tut1.183216
ohope4Doctahemioctahedron prism1.118034
ohopy, pt || oho4D(degenerate)octahemioctahedron pyramid∞   i.e. flat in euclidean space
ohuhoh4Doctihexadecahemihexadecachoron1
oid5Doctagon-icosidodecahedron duoprism2.079697
oike5Doctagon-icosahedron duoprism1.616049
omfapaxady4Domnicircumfacetopental hexacosadishecatonicosachoron0.726543
ondip4Doctagonal spinoduoprism1.485633
...4Dmedial tetrastratic segment oftelex
...4Dooofxfooo3xoxxoxxox5ofxofoxfo&#xt
...4DooofxxFfooFoofo3oxFxoFxxxFooFxx3xfoxFoofFxxFoox&#xt
...4DooofxxFfooFxofx3oxFxoFxxxFoxFxo3xfoxFoofFxxfooo&#xt
...4Doooxfxooo3xoxoxoxox5ofxfofxfo&#xt
...4Dooxf3xfox3oxFx&#xt
op3Doctagonal prism, bidiminishedsmall rhombicuboctahedron1.398966
opatic, op || tic, K-4.1064Doctagonal prism atoptruncated cube1.847759
ope, K-4.11 (alt: dytpuf)4Doctahedron prism,vertex figure ofrat, dyadictegmipucofastegium, equatorial cross-section oftet-firstdot0.866025
opeaco5Doctahedron-prism atopcuboctahedron, diminished1/4-lune of rat1
opeacope5Dope atopcope,octaco-prism,ope-first half oficope1.118034
opeah5Dope atop hexagon, (trip,gyrotrip,hexagon)-trigonic1
opeatut (alt.: octoct tuttric)5Dope atoptut, (oct,oct,tut)-trigonic1.190238
opeatuttip5Dope atoptuttip,octatut-prism,ope-first cap ofsrippip1.284523
open6Doctagon-pentachoron duoprism1.451588
opepy5Doctahedral-prismatic pyramid, vertex pyramid ofrectified triacontiditeron1
opet5Doctahedral-prismtegum, (line,octahedral prism)duotegum...
...3Doq ou&#hsquippy variant1.224745
...4Dpentachoron-derived Gévay polychoron, rectifiedo3m3o3o1.095445
...4Dhexacosachoron-derived Gévay polychoron, rectifiedo3m3o5o6.412847
...3DWaterman polyhedron number 5 wrt. body-centered cubiclattice C3* centered at a lattice point, slightly chamferedcube,octahedrally shallow truncatedrhombic dodecahedron
...4DWaterman polychoron number 5 wrt. primitive tesseracticlattice C4 centered at a hole3
...4DWaterman polychoron number 5 wrt. primitive tesseracticlattice C4 centered at a lattice point
...3Doq4oo&#hsquippy variant1.060660
...3Delongated hexagonal dipyramid
...3Drectified/ambifiedn/d-prism,o o-n/d-o symmetricco relative1/[sqrt(2) sin(π d/n)]
...3Doqo3ooq&#xt, cubera (cube chimera), (fully) mono-truncatedcube0.866025
osirco5Doctagon small-rhombicuboctahedron duoprism1.914214
osquat2Dhyperbolic order 8 square tiling0.321797i
osrid5Doctagon - small-rhombicosidodecahedron duoprism2.587117
ostodip4Doctagon-octagram duoprism1.414214
otacoh3Dhyperbolic x3x4x3x4*a tesselation, omnitruncated cubic-octahderal honeycomb2.197368i
otathisbit4Domnitruncated-trihexagonal-square duoprismatic tetracomb
otbaquitit4Doctagonnally tetrablended quasitruncated tesseract0.615370
otbott4Doctagonnally tetrablended truncated tesseract2.149726
otcyloh6Domnitruncated cycloheptapetic hexacomb,Voronoi complex oflattice A6*
otcypit4Domnitruncated cyclopentachoric tetracomb, great-prismatodecachoric tetracomb,Voronoi complex oflattice A4*
otet5Doctagon-tetrahedron duoprism, octagon duofastegium1.442951
oti5Doctagon - truncated-icosahedron duoprism2.801372
otic (old: ottic)5Doctagon - truncated-cube duoprism2.207107
otid5Doctagon - truncated-dodecahedron duoprism3.244185
otitch3Dhyperbolic x3x3x3x4*a tesselation, omnitruncated tetrahedral-cubic honeycomb2.942253i
otoe (old: otto)5Doctagon truncated-octahedron duoprism2.051123
otrat2Dhyperbolic order 8 triangular tiling0.594604i
otratip3Dhyperbolic x x3o8o tesselation0.321797i
otut5Doctagon - truncated-tetrahedron duoprism1.755593
otwadip4Doctagon - dodecagon duoprism2.332200
owau prit   (alt.: pox spic, alt.: phic prico)4Docta-augmentedprismatorhombated tesseract, partially octa-expandedsmall prismated (dis)icositetrachoron, partially hexadeca-contractedprismatorhombated icositetrachoron
owaudope4Domni-augmenteddodecahedral-prism
owoct5Doctagon octahedron duoprism1.485633
...4Dox3/2ox3xo&#x0.707107
...3DWaterman polyhedron number 4 wrt. face-centered cubiclattice A3 centered at a shallow hole1.837117
...3Dvertex figure ofthex0.948683
...3Dvertex figure ofope0.816497
...3D20thawroes toroid
...4DoxFxofo3xfoxFxx3ooxfoox&#xt   (F=ff=x+f)
...6D(mono)tetal tratet augmentedtetdip0.866025
...7Doxo3ooo3ooo3xoo3ooo3oxx&#xt1
...4Doxofofoxo3oofoxofoo5xxoxxxoxx&#xt
...4Doxofxfooo3xxxxoxxox5ooxofoxfo&#xt
...4Doxofxfoxo3xxFxoxFxx5xxoxFxoxx&#xt
...4Doxofxfoxo3xxxxoxxxx5ooxofoxoo&#xt
...4Doxoofooxo3oofxoxfoo5xxoxxxoxx&#xt
...4Doxoxfxooo3xxxoxoxox5ooxfofxfo&#xt
...4Doxoxfxoxo3xxxoxoxxx5ooxfofxoo&#xt
...4Doxqw wxwx3ooxx4qwox&#zx
...4DoxqwQ wxwxx3ooxxx4qwoxo&#zx
...3Doctagonal Leonardo style "polyhedron of renaissance",vertex figure oflamina-trunc(o8o4xb3x)1.847759
...4Dproh-cap augmentedbistratic prit-cap...
...4DoxwQ wxoo3xxxx4oxxo&#zx...
...4Dpoint atoptet atopco
...4Doct atoptut atoptoe
...4DoxxFxoAFxxFoxFx3xofxxFoooFxxfox3xFxoFxxFAoxFxxo&#xt

P

...3Dcomplex polyhedronxp   x2-3-o2
...3Dcomplex polyhedronxp   x3-3-o3sqrt[2+1/sin2(π/p)]
...3Dcomplex polyhedronxp   xr   xt
...3Dcomplex polyhedronxp   xr-4-o2,complex polyhedronxp   xr   xr
...3Dcomplex polyhedronxp   xr || op   xr
...3DShephard'sp-generalised cube,complex polyhedronxp-4-o2-3-o2, γp3sqrt(3)/(2 sin(π/p))
...4DShephard'sp-generalised tesseract,complex polychoronxp-4-o2-3-o2-3-o2, γp4
...2Dcomplex honeycombxp-4-o2-4-o2, δp,23,complex honeycombo2-4-xp-4-o2,complex honeycombxp-4-o2-4-xp
...2Dcomplex honeycombxp-4-o2-4-op, δp,p3
...2Dcomplex honeycombxp-4-o2-4-or, δp,r3
...2Dcomplex honeycombxp1-q1-or1   xp2-q2-or2, δp1,r12 × δp2,r22
...3Dp12-h4
...3Dpentagonal antidipyramid, pentagonal antitegum, pentagonal kiteohedron, dual ofpap, axial bi-kis-doe, deca-truncatedsissid
pabac carnit5Dpartially bicontractedcellirhombated penteractitriacontiditeron...
pabac scant5Dpartially bicontractedsmall cellated penteractitriacontiditeron...
pabac sirn5Dpartially bicontractedsmall rhombated penteract...
pabac span5Dpartially bicontractedsmall prismated penteract...
pabacca pin5Dpartially bicontractedcelliprismated penteract...
pabaud, J593Dparabiaugmented dodecahedron
pabauhip, J553Dparabiaugmented hexagonal prism
pabautid, J693Dparabiaugmented truncated dodecahedron
pabdi skiviphado4Dparabidiminishedsmall skewverted prismatohexadecadisoctachoron1.414214
pabdico4Dparabidiminishedicositetrachoron, hexa-augmentedtesseract1
pabdimo, dot||scad||dot6Dparabidiminishedmo,dodecateron atop pseudosmall cellated dodecateron atopdodecateron1
pabdiproh4Dparabidiminishedprismatorhombated hexadecachoron, tristratictic-first central segment ofproh2.613126
pabdirico4Dparabidiminishedrectified icosatetrachoron, bistraticco-first central segment ofrico, axis-orthogonal partial Stott expandedrit1.732051
pabditoe3Dparabidiminishedtruncated octahedron1.581139
pabex gyetac5Dpartially bi-expandedgyroelongated-triacontaditeron...
pabex hax6Dpartially biexpandedhemihexeract,truncated tetrahedralduoalterprism1.658312
pabex hix (alt.: thiddipcup)5Dpartially bi-expandedhexateron,thiddip cupoliprism1.190238
pabex rat5Dpartially biexpandedrectified triacontiditeron...
pabex sart5Dpartially biexpandedsmall rhombated triacontiditeron...
pabex tac5Dpartially biexpandedtriacontaditeron...
pabex thex4Dpartially biexpandedtruncated hexadecachoron, partially bicontractedprismatorhombated tesseract...
...3Dpartially bi-expandedhyperbolic order 8 triangular tiling, partially bi-contractedhyperbolic shieldotritetragonal tiling
pabexnit5Dpartially biexpandedpenteractitriacontiditeron...
pabexrico4Dpartially bi-expandedrico, partially bi-contractedproh
pabexrit4Dpartially bi-expandedrit, partially bi-contractedtat
pabextah4Dpartially bi-expandedtesseractihexadecachoron, partially bi-contractedgreat rhombated tesseract
pabextet3Dpartially bi-expandedtetrahedron
pabextico4Dpartially bi-expandedtico, partially bi-contractedgidpith
pabextot5Dpartially biexpandedtruncated triacontaditeron...
pabextut3Dpartially bi-expandedtruncated tetrahedron
pabgyrid, J733Dparabigyrated rhombicosidodecahedron2.232951
pabgysiphin5Dparabigyratedsmall-prismated-hemipenteract1.274755
pabidrid, J803Dparabidiminished rhombicosidodecahedron2.232951
pac gidpith4Dpartially (mono-)contractedgidpith
pac girco3Dpartially (mono-)contractedgreat rhombicuboctahedron...
pac grit4Dpartially (mono-)contractedgreat rhombated tesseract
pac scant5Dpartially contractedsmall cellated penteractitriacontiditeron...
pac span5Dpartially contractedsmall prismated penteract...
...2Dpartially contractedhyperbolic order 3 tritetragonal tiling
...3Dpartially contractedhyperbolic shieldotritetragonal tiling
...3Dpartially contracted hyperbolicx4o3x3o3*b tesselation
...3Dpartially contracted hyperbolicx4o3x3x3*b tesselation
pacca pin5Dpartially contractedcelliprismated penteract...
paccarnit5Dpartially contractedcellirhombated penteractitriacontiditeron...
pacop3Dpartially Stott contractedoctagonal prism
pacprich3Dpartially contractedprismatorhombated cubic honeycomb
pacprit4Dpartially (mono-)contractedprit...
pacproh4Dpartially (mono-)contractedproh
pacratoh3Dpartially contractedruncinated tetrahedral-octahedral honeycomb
pacrothat2Dpartially contractedrhombitrihexagonal tiling
pacsid pith (alt: cuba sircobcu)4Dpartially (mono-) contractedsidpith, partially expandedquawros,cubasirco bicupola
pacsirn5Dpartially contractedsmall rhombated penteract...
pacsrich3Dpartially contractedsmall rhombated cubic honeycomb
pacsrit4Dpartially (mono-)contractedsmall rhombated tesseract...
pactat4Dpartially (mono-)contractedtat
pactic3Dpartially (mono-)contractedtruncated cube...
padedip4Dpentagon - decagon duoprism1.828016
padex snic3Dpartially dodeca-expandedsnub cube
padiap4Dprismatic double inverted antiprism, pentagrammic double antiprismoid0.618034
padohi4Dprismatodishecatonicosachoron2.497212
..., padohi || rofix5D(degenerate)padohi atoprofix∞   i.e. flat in euclidean space
paf, K-4.224Dpentagonal antifastegium, pentagon -pap wedge, {5} || gyropip1
pafirp4Dpartially facetedrap, reduced3tet atop2thah self-blend,tet atop "squares ofthah"0.774597
pagydrid, J773Dparagyrate diminished rhombicosidodecahedron2.232951
pahtex prit4Dpartially demitesseractic-expandedprit, partially demitesseractic-contractedgidpith
pahtex sidpith4Dpartially demitesseractic-expandedsidpith, partially demitesseractic-contractedproh
pahtex srit4Dpartially demitesseractic-expandedsrit, partially demitesseractic-contractedgrit
pahtex tes4Dpartially demitesseractic-expandedtesseract, partially demitesseractic-contractedtruncated tesseract, hexadecachorally truncatedtesseract
pakid3Dpentakis dodecahedron, apiculated dodecahedron
paltite4Dprismatoaltitruncatedico tetracomb
pap3Dpentagonal antiprism, para-bidiminishedicosahedron0.951057
...4Ddodecaswirlic triacosihexacontachoron, thirtyfold dissecteddodecahedral polytwister, thirtyfold dissected doter...
papadoe, pap || doe, K-4.814Dpentagonal-antiprism atopdodecahedron, parabidiminished segment of vertex-firsthexacosachoron,pentagonal-antiprism-first cap ofgrand antiprism1.618034
papaid, pap || id, K-4.1424Dpentagonal-antiprism atopicosidodecahedron3.077684
paphacki4Dpentagon-prismatic heptacosicosachoron, great prismasaurus (also: great prismosaurus)1
paphicki4Dpentagram-prismatic heptacosicosachoron, small prismasaurus (also: small prismosaurus)1
pappip, K-4.394Dpentagonal-antiprism prism1.074481
pappy4Dpentagon-antiprismatical pyramid1.618034
papvixhi4Dpentagonal prismatoverted hexacosahecatonicosachoron1.902113
paqri4Dprismatoquasirhombated icositetrachoron1.938391
paqrich3Dprismated quasirhombated cubic honeycomb
paqrigafix (old: paquerfix)4Dprismatoquasirhombated great facetted hexacosachoron1.878261
paqrigagishi (old: paqrahi)4Dprismatoquasirhombated great grand stellated hecatonicosachoron1.207883
paqrigshi (old: paqraghi)4Dprismatoquasirhombated great stellated hecatonicosachoron (prismatoquasirhombated grand hecatonicosachoron)3.199386
paqrit4Dprismatoquasirhombated tesseract1.174172
...3Dpara bi lowered truncated cube...
passipsi3Dpseudosnub pentagrammattic snub (pseudo)icosiicosahedron,compound of 5sissid0.587785
passipsido3Dpseudosnub pentagrammatic snub (pseudo)disoctahedron,compound of 2sissid0.587785
pataht4Dprismatotruncated demitesseractic tetracomb, prismatodiprismatodisicositetrachoric tetracomb, runcitruncated hexadecachoric tetracomb
patal6Dprismatotruncatedheptapeton, runcitruncated heptapeton2
patex sirco3Dpartially tetrahedrally-expanded small rhombicuboctahedron, tetrahedrally lowered small rhombicuboctahedron, partially tri-expanded truncated tetrahedron...
paticot4Dprismatotruncated icositetrachoric tetracomb, small diprismatodisicositetrachoric tetracomb, runcitruncated icositetrachoric tetracomb
patom (old: kaprom)6Dprismatotruncatedpentacontitetrapeton, runcitruncated pentacontitetrapeton, (heptacontidiprismatorhombated pentacontitetrapeton)3.872983
pattin5Dprismatotruncatedpenteract, runcitruncated penteract3.239235
pattit5Dprismatotruncatedtriacontiditeron, runcitruncated pentacross2.738613
pattix5Dprismatotruncatedhexateron, runcitruncated hexateron1.848423
pautpen4Dpenta-augmentatedtruncated pentachoron...
paw, K-4.1334Dantipentawedge, decagon -pentagon-antiprismatic wedge, pentagonal gyrobicupolaic ring, {10} ||pap, {5} || gyratedpecu3.077684
pd{3,5,3}3Dpartial diminishing (old: truncation) of hyperbolicorder 3 icosahedral tesselation0.509376i
peat2Dhyperbolic order 4 pentagonal tiling0.899454i
peatip3Dhyperbolic x x5o4o tesselation0.747674i
pechon3Dhyperbolic order 5cubic honeycomb0.555893i
peco5Dpentagon-cuboctahedron duoprism1.312862
pecu, J53Dpentagonal cupola2.232951
pecube5Dpentagon-cube duoprism1.213922
pecuf, K-4.1544Dpentagonal cupofastegium, decagon -pentagon-prismatic wedge, pentagonal orthobicupolaic ring, {10} ||pip, {5} ||pecu, 2/5-luna ofstawros5.236068
pecupe4Dpentagonal-cupola prism,pentagonal-prism atopdecagonal-prism2.288246
pedap4Dpentagonal duoantiprism...
pedecat2Dhyperbolic order 5 decagonal tiling0.154508i
pedhon3Dhyperbolic order 5dodecahedral honeycomb0.427486i
pedip4Dpentagon-pentagon duoprism1.203002
pedisna4Dpental disnubbachoron,compound of 12ex inrox army,compound of 2kepisna1.618034
...3Dvertex figure ofpental disnubbachoron, biform twirledcompound of 2 vertex-firsticosahedra0.951057
pedoe5Dpentagon-dodecahedron duoprism1.639247
pedpedip4Dpentadiminishedpentagonal duoprism1.203002
pedpy (alt.: pet), J133Dpentagonal dipyramid, (line-)pentagon-tegum
pedril (alt.: squatratet)6Dpentadiminishedrectified heptapeton, square atoptratet0.845154
pegybcu, J313Dpentagonal gyrobicupola
pegycuro, J333Dpentagonal gyrocupolarotunda
pehi6Dpentagon - hecatonicosachoron duoprism3.798922
pen, K-4.14Dpentachoron, 4Dsimplex (α4), 5-cell, pyroter(id),tetrahedral pyramid, triangle-pyramidal pyramid, regular triangle-scalene, regular line-tettene, regular (point-)pennene, 3tet rosette,vertex figure ofhix,Gosset polytope 03, 5-2-stepprism0.632456
penaf (old: penalpenp)6Dpentachoron antifastegium,pentachoron atop invertedpentachoral-prism,pen-first cap ofjak0.816497
penal rappip6Dpen-first cap ofpentacontitetrapeton1
penalsrip, pen || inv srip5D(degenerate)pen atop invertedsrip∞   i.e. flat in euclidean space
penarappip6Dpen-first cap ofbirectified heptapeton0.925820
penaspid5Dpentachoron atopsmall prismated decachoron,pen-firstrotunda ofscad1
penasrip5Dpen atopsrip1.274755
penatrip5Dpentachoron atoptrigonal prism, (edge,perp triangle,trip)-trigonic1
pendip8Dpentachoron duoprism,vertex figure oficoy0.894427
penhex8D(pentachoron,hexadecachoron)-duoprism,vertex figure ofnav0.948683
penhix9Dpentachoron -hexateron duoprism,vertex figure ofteru0.903696
penit (old: pendpy)5Dpentachoral (line-)tegum, pentachoral dipyramid
pennatip5Dpen atoptip,pen-first cap ofrin1.414214
penp5Dpentachoron prism,vertex figure ofril0.806226
penpal rappip6Dpenp atop alternaterappip,dihin prism0.935414
penpasc7Dpentachoron-prismaticscalene,pentachoron-prism-pyramid pyramid, line atop fully orthogonalpentachoron prism0.935414
penppy6Dpenp pyramid, vertex-pyramid ofril0.845154
penrap8D(pentachoron,rectified pentachoron)-duoprism,vertex figure of tergoh1
penrapdit8D(pen,rap)-duotegum,tegum product ofpentachoron andrectified pentachoron
pent5Dpenteract, decateron, 5Dmeasure-polytope (γ5), geopet(id)1.118034
pentanit6Dpent atopnit1.228783
pentarin6Dtesseract atoprectified tesseract1.418705
pente (old: pennit)4Dhyperbolic order 5pentachoric tetracomb0.393076i
penth (alt.: stenoh)5Dpenteractic pentacomb, 5Dhypercubical honeycomb (δ5), (alt.: small terated penteractic pentacomb)
penu5Dpentachoron-based ursateron,pen-basedursulate,vertex figure ofo3o3o3o4s3s1.029086
pepat2Dhyperbolic order 5 pentagonal tiling0.528686i
pepip5Dpentagon duoprismatic prism1.302772
peppia pero, K-4.1394Dpentagonal-pyramid atoppentagonal-rotunda3.077684
peppy, 5pyr, J23Dpentagonal pyramid0.951057
peppyp, K-4.384Dpentagon-pyramidal prism, J2 prism, line ||pip1.074481
pepuf, K-4.1654Dpentagonal pucofastegium, pentagon -decagon-prismatic wedge, pentagonal magnabicupolaic ring, {5} ||dip, {10} ||pecu, {5}-first cap ofsrahi6.735034
pero, J63Dpentagonal rotunda, half oficosidodecahedron1.618034
perope, K-4.924Dpentagonal-rotunda prism1.693527
pesc (old: peppypy), K-4.864Dpentagonscalene, pentagon-pyramidal pyramid, line atop fully orthogonal pentagon, 5tet rosette1.618034
pesquat2Dhyperbolic order 5 square tiling0.747674i
petet5Dpentagon-tetrahedron duoprism, pentagon duofastegium1.048144
pettip6Dpentagon-pentagon-pentagon-triprism1.473370
pex hex4Dpartially (mono-)expandedhex, partially contractedquawros
pex rat5Dpartially expandedrectified triacontiditeron...
pex sart5Dpartially expandedsmall rhombated triacontiditeron...
pex tac5Dpartially expandedtriacontaditeron...
pex thex4Dpartially (mono-)expandedthex...
...3Dpartially extended hyperbolico4o3x3o3*b tesselation
...3Dpartially extended hyperbolico4o3x3x3*b tesselation
...3Dpartially expandedhyperbolic order 8 triangular tiling
pexco3Dpartially (mono-)expandedcuboctahedron, 4fold elongatedcuboctahedron...
pexgyetac5Dpartially expandedgyroelongated-triacontaditeron...
pexhax6Dpartially expandedhemihexeract,tetrahedral-truncated-tetrahedralduoalterprism1.322876
pexhin (old: tutas)5Dpartially expandedhemipenteract,truncated tetrahedronaltersquarism,tuta alterprism, cyclodiminishedsiphin1.274755
pexhix (alt.: triddipah, tripotricudaw)5Dpartially expandedhexateron,triangle-triangle duoprism atophexagon, (trip,tricu)-disphenoid, (trip,tricu)-duopyramid1
pexic4Dpartially (mono-)expandedicositetrachoron...
pexnit5Dpartially expandedpenteractitriacontiditeron...
pexrich3Dpartially expandedrectified cubic honeycomb
pexrico4Dpartially (mono-)expandedrico
pexrit4Dpartially (mono-)expandedrit
pextah4Dpartially (mono-)expandedtesseractihexadecachoron
pextet3Dpartially (edge-)expandedtetrahedron
pextich3Dpartially expandedtruncated cubic honeycomb
pextico4Dpartially (mono-)expandedtico
pextoe3Dpartially (mono-)expandedtruncated octahedron...
pextoh3Dpartially expandedtetrahedral-octahedral honeycomb
pextot5Dpartially expandedtruncated triacontaditeron...
pextrat2Dpartially expandedtriangular tiling
pextut3Dpartially (edge-)expandedtruncated tetrahedron
phap5Dpentachoric hemiantiprism0.707107
phat2Dhyperbolic pentahexagonal tiling0.786151i
phexah3Dhyperbolic order 5hexagonal-tiling honeycomb0.381966i
phexdo3Dpartially hexa-expandeddodecahedron
phexid3Dpartially hexa-expandedicosidodecahedron
phexik3Dpartially hexa-expandedicosahedron
phiddip4Dpentagon hexagon duoprism1.312862
phitte4Dhyperbolic order 5hecatonicosachoric tetracomb0.206652i
phud4Dprismatohemidecachoron1
pibhaki4Dpentagonal-bipyramidal heptacosiicosachoron,rectified-hexacosachoron dual, surtegmated hecatonicosachoron
pibox srico4Dpartially bi-octa-expandedsmall rhombitetracontoctachoron
pibox tico4Dpartially bi-octa-expandedtruncated icositetrachoron
picnut4Dprismatocubiintercepted tesseract0.890446
pid5Dpentagon - icosidodecahedron duoprism1.828016
piddaf5Dpentagonal duoantifastegium, (2,5)-duoantiwedge,pip atop bidualpip1.014647
pikap (alt.: snittap)4Dpyritohedral icosahedral antiprism, snub-tetrahedral antiprism, non-uniform alternation oftope...
pike5Dpentagon-icosahedron duoprism1.275976
pinnip4Dprismatointercepted pentachoron, retropyroinvertirectichoron,vertex figure ofhan0.774597
...4Dpinnip+5 2thah (?)0.774597
pinnipdip4Dpentaintercepted prismatodispentachoron, prismatopentaintercepted dispentachoron1.183216
...4Dpinnipdip+15{4} (?)1.183216
pinpith4Dprismatointercepted prismatotesseractihexadecachoron1.847759
...4Dpinpith+48{4}1.847759
pinpixhi4Dprismatointercepted prismatohexacontahecatonicosachoron6.735034
...4Dpinpixhi+1800{4} (?)6.735034
pip3Dpentagonal prism, 5-p,vertex figure ofrox0.986715
piphid4Dprismatopentahemidecachoron, copyrofacetoretropodichoron1
...4Dpiphid+10tet (?)1
pippindip4Dprismatopentintercepted dispentachoron1.183216
pippy, K-4.1414Dpentagonal-prismatic pyramid, vertex pyramid of therectified hexacosachoron3.077684
pirgadia5Dpirgady alterprism1.125151
pirgady4Dpseudorhombated great dishecatonicosachoron1.054256
pirgaghi4Dprismatorhombated great grand hecatonicosachoron1.893038
pirghi4Dprismatorhombated great hecatonicosachoron4.917351
pirghia5Dprismatorhombated great hecatonicosachoron alterprism4.923348
pirhatit4Dprismatorhombated demitesseractic tetracomb, great prismatodemitesseractic tetracomb, steriruncic tesseractic tetracomb
pirhin5Dprismatorhombatedhemipenteract, runcicantellated demipenteract, steriruncicpenteract2.150581
pirpop4Dpseudorhombated prismatopentachoron1.183216
...4Dpirpop+5 2thah (?)1.183216
pirsady4Dpseudorhombated small dishecatonicosachoron6.073594
pirshi4Dprismatorhombated (small) stellated hecatonicosachoron5.515107
pirt5Dprismatorhombatedtriacontiditeron, runcicantellated pentacross3
pirx5Dprismatorhombatedhexateron, runcicantellated hexateron1.914854
pistadedip4Dpentagon - decagram duoprism1.051462
pistodip4Dpentagon - octagram duoprism1.008216
pitest4Dhyperbolic order 5tesseractic tetracomb0.242934i
pithatit4Dprismatotruncated demitesseractic tetracomb, small prismatodemitesseractic tetracomb, stericantic tesseractic tetracomb
pithax6Dprismatotruncatedhemihexeract, runcitruncated demihexeract, stericantichexeract2.958040
pithin5Dprismatotruncatedhemipenteract, runcitruncated demipenteract, stericanticpenteract2.371708
pittip4Dprismatotriakispentachoron1.612452
pobcu, J303Dpentagonal orthobicupola
pobro, J343Dpentagonal orthobirotunda1.618034
poc gippic4Dpartially octa-contractedgreat prismatotetracontoctachoron
poc prico   (alt.: phex spic)4Dpartially octa-contractedprismatorhombated icositetrachoron, partially hexadeca-expandedsmall prismated (dis)icositetrachoron...
poccont4Dpartially octa-contractedtetracontoctachoron
pocsric   (alt.: phixic)4Dpartially octa-contractedsmall rhombated icositetrachoron, partially hexadeca-expandedicositetrachoron, octa-augmentedtruncated tesseract...
poct5Dpentagon - octahedron duoprism1.106168
pocuro, J323Dpentagonal orthocupolarotunda
...4Dpocuro wedge...
podip4Dpentagon - octagon duoprism1.559075
potag6Dprismatotruncatedhexacontitetrapeton, runcitruncated hexacross2.738613
potatit4Dprismatotruncated tesseractic tetracomb, small tomocubic-diprismatotesseractic tetracomb, runcitruncated tesseractic tetracomb
potax6Dprismatotruncated hexeract, runcitruncated hexeract3.762560
pox prico4Dpartially octa-expandedprismatorhombated icositetrachoron
pox rico4Dpartially octa-expandedrectified icositetrachoron
pox snic3Dpartially octa-expandedsnub cube
pox srico4Dpartially octa-expandedsmall rhombated icositetrachoron
pox tico4Dpartially octa-expandedtruncated icositetrachoron
poxic   (alt.: phic srico, alt.: owau sidpith)4Dpartially octa-expandedicositetrachoron, partially hexadeca-contractedsmall rhombated icositetrachoron, octa-augmentedsmall diprismated tesseractithexadecachoron...
prahi4Dprismatorhombatedhecatonicosachoron, runcitruncatedhexacosachoron8.278950
..., prahi || grix5D(degenerate)prahi atopgrix∞   i.e. flat in euclidean space
prahip (old: prahipe)5Dprismatorhombated-hexacosachoron prism, runcitruncated-hexacosachoron prism8.294035
praht4Dprismatorhombated demitesseractic tetracomb, great tetracontaoctachoric tetracomb, runcicantellated hexadecachoric tetracomb
prap vixhi4Dpentagonal retroprismatoverted hexacosahecatonicosachoron1.175571
praquinoh5Dprismatorhombated quarterpenteractic pentacomb
prarsi4Dprismatorhombiretrosnub icositetrachoron1.328131
presipsi3Dpseudoretrosnub pentagonal snub (pseudo)icosiicosahedron,compound of 5gad0.951057
presipsido3Dpseudoretrosnub pentagonal snub (pseudo)disoctahedron,compound of 2gad0.951057
pretasto4Dpentagonorhombic trisnub trisoctachoron
prich3Dprismatorhombated cubic honeycomb, runcitruncated cubic honeycomb
prico4Dprismatorhombatedicositetrachoron, runcitruncated icositetrachoron3.498949
..., prico || gyro grico5D(degenerate)prico atop gyratedgrico∞   i.e. flat in euclidean space
pricoa (old: pricoalprico)5Dprismatorhombated-icositetrachoron alterprism,prismatorhombated-icositetrachoron atop alternateprismatorhombated-icositetrachoron3.522336
pricope (old: pripe)5Dprismatorhombated-icositetrachoron prism, runcitruncated-icositetrachoron prism3.534493
pricot4Dprismatorhombated icositetrachoric tetracomb, great diprismatodisicositetrachoric tetracomb, runcicantellated icositetrachoric tetracomb
priddoh3Dhyperbolic prismatorhombated (order 4) dodecahedral honeycomb, hyperbolic prismatotruncated order 5 cubical honeycomb, hyperbolic runcitruncated order 5 cubical honeycomb2.878623i
prih3Dhyperbolic prismatorhombated order 3 icosahedral honeycomb, hyperbolic runcitruncated order 3 icosahedral honeycomb2.809263i
pril6Dprismatorhombatedheptapeton, runcicantellated heptapeton2.104417
prin5Dprismatorhombatedpenteract, runcicantellated penteract3.047217
prip4Dprismatorhombatedpentachoron, runcitruncated pentachoron1.612452
pripa (old: pripalprip)5Dprip alterprism,prip atop invertedprip, medial segment ofcard1.658312
pripa gippid5Dprip atopgippid,prip-first cap ofpattit2.738613
pripagrip5Dprip atopgrip1.870829
pripal gripu5D(prip,grip)-based ursateron1.904375
pripalgrip5Dprip atop alternategrip1.848423
pripech3Dhyperbolic prismatorhombated order 5 cubic honeycomb, hyperbolic prismatotruncated order 4 dodecahedral honeycomb, hyperbolic runcicantellated order 5 cubic honeycomb, hyperbolic runcitruncated order 4 dodecahedral honeycomb3.081165i
pripped3Dhyperbolic prismatorhombated order 5 dodecahedral honeycomb, hyperbolic runcitruncated order 5 dodecahedral honeycomb2.212971i
prippip5Dprismatorhombated-pentachoron prism1.688194
pripro5Dprip-firstrotunda ofcaptid2.236068
prishi4Dprismatorhombisnub hecatonicosachoron3.625437
prisquah4Dhyperbolic prismatorhombatedsquare-tiling honeycomb, hyperbolic prismatotruncated order 4 octahedral honeycomb, hyperbolic runcitruncated order 4 octahedral honeycomb2.345208i
prissi4Dprismatorhombisnub icositetrachoron, prismato-semistruncated icositetrachoron, runcic snub icositetrachoron2.497212
prissia5Dprismatorhombisnub icositetrachoric alterprism, triangle-alternation ofprismatorhombated icositetrachoric prism3.534493
prissibich, 5Y4-3T-3Q3-T34Dprismatorhombisnub bicubic honeycomb
pristrah4Dhyperbolic prismatorhombisnubtriangular-tiling honeycomb, hyperbolic runcisnub triangular tiling honeycomb, edge-alternated hyperbolicprismatorhombated triangular-tiling honeycomb...
prit4Dprismatorhombated tesseract, prismatotruncated hexadecachoron, runcitruncated hexadecachoron2.370932
..., prit || grit5D(degenerate)prit atopgrit∞   i.e. flat in euclidean space
pritrah3Dhyperbolic prismatorhombatedtriangular-tiling honeycomb1.931852i
prittip5Dprismatorhombated-tesseract prism, prismatotruncated-hexadecachoron prism, runcitruncated-hexadecachoron prism, central segment ofcappin2.423081
prittit4Dprismatorhombated tesseractic tetracomb, rhombitesseractic-diprismatotesseractic tetracomb, runcicantellated tesseractic tetracomb
prix4Dprismatorhombated hexacosichoron, runcitruncated hecatonicosachoron9.744610
prixip5Dprismatorhombated-hexacosachoron prism, runcitruncated-hexacosachoron prism9.757429
prog6Dprismatorhombatedhexacontitetrapeton, runcicantellated hexacross3
proh4Dprismatorhombatedhexadecachoron, prismatotruncatedtesseract, runcitruncated tesseract2.613126
..., proh || gidpith5D(degenerate)proh atopgidpith∞   i.e. flat in euclidean space
prohagrit5Dproh atopgrit,proh-first segment ofpattin3.239235
prohalsrico5Dproh atopsrico2.632865
prohax6Dprismatorhombatedhemihexeract, runcicantellated demihexeract, steriruncichexeract2.783882
prohp5Dprismatorhombated-hexadecachoron prism, prismatotruncated-tesseract prism, runcitruncated-tesseract prism, central segment ofcarnit2.660531
prom (old: kaptom)6Dprismatorhombatedpentacontitetrapeton, (heptacontidiprismatotruncated pentacontitetrapeton)4.582576
prox6Dprismatorhombatedhexeract, runcicantellated hexeract3.598576
...4D(0,0,0,12,0)-diminished vertex-first-rotunda of ex, dodeca-diminished vertex-firstrotunda ofhexacosachoron1.618034
pta cubaike4Dcube-augmentedcubaike1
ptaika cube4Dike-augmentedcubaike
puko8Dpetiskewed octeract1.732051
puph7Dpetaprismated hexadecaexon1.732051
pybiscrox4D pyritohedral bistraticicosahedron-first cap ofrectified hexacosachoron3.077684
pysna4Ds2s3s4x, pyritosnub alterprism, edge-alternatedgreat-rhombicuboctahedronal prism, edge-snub octahedral hosochoron...
pysnan5Dpyritosnub penteract, edge-alternation ofgreat cellated penteractitriacontiditeron...
pysnet4Ds3s3s4x, pyritosnubtesseract, edge-alternatedgreat diprismated tesseractihexadecachoron, edge-snubhexadecachoron...
pysneta5Dpyritosnub tesseractic alterprism, edge-snub hexadecachoric hosoteron...
pysnic3Dpyritosnub cube, pyritohedralsirco variant, hexadiminishedid1.618034
pysnic3Dpyritosnub cube, pyritohedralsirco variant, facetedtigid1.876844
pysnic3Dpyritosnub cube, pyritohedralsirco variant, edge-alternatedgirco2.317611
pystid3Dpyritohedrally stellatedicosidodecahedron

Q

...3Dq x3o, variation oftriangular prism,vertex figure ofrectified tesseract0.912871
...4Dq x3o3o, variation oftetrahedron prism,vertex figure ofrectified penteract0.935414
...5Dq x3o3o3o, variation ofpentachoron prism,vertex figure ofrectified hexeract0.948683
...3Dq x4o, variation ofcube,vertex figure ofrectified cubic honeycomb1
...3Dq x5o, variation ofpentagonal prism1.106168
...3Dq x6o, variation ofhexagonal prism1.224745
...3Dq x8o, variation ofoctagonal prism1.485633
...4Dq3o3o4x, variation ofsidpith1.732051
...3Dq3o3x, variation ofcuboctahedron1.215958
...4Dq3o4o3x, variant ofspic2.236068
...3Dq3o4x, variation ofsmall rhombicuboctahedron, hull oftisso1.658312
...3Dq3o5x, variation ofsrid2.601518
...3Dq3q4x,Waterman polyhedron number 5 wrt. primitive cubiclattice C3 centered at a hole, variation ofgirco2.958040
...3Dq3x3o, variation oftruncated tetrahedron, triangle-snubsmall rhombicuboctahedron1.398966
...3Dq3x4x, variation ofgirco, hull ofquitco2.564844
...3DQo oq4xx&#zh, variation ofsquobcu
...3Dqo oq&#h, longer variant ofdigonal antiprism,vertex figure ofbatch1
...3Dqo ou&#h disphenoid1.224745
...4Dqo3oo3oo&#x, shallower variant oftetrahedral pyramid, vertex pyramid oftes1
...4DWaterman polychoron number 4 wrt. primitive tesseracticlattice C4 centered at a hole2.645751
...3DWaterman polyhedron number 4 wrt. primitive cubiclattice C3 centered at a hole, cubicallyexpandedrhombic dodecahedron2.598076
...3Dqo3oo&#h, taller variant oftrigonal pyramid,vertex figure oftico0.981981
...3Dqo3oo&#x, shallower variant oftrigonal pyramid, vertex pyramid ofcube0.866025
...4Dqo3oq3oo&#x, shallower variant ofrap, segment oftes1
...3DWaterman polyhedron number 7 wrt. body-centered cubiclattice C3* centered at a lattice point
...3Dqo3oq&#x, shallower variant oftrigonal antiprism, medial segment ofcube0.866025
...3DWaterman polyhedron number 8 wrt. body-centered cubiclattice C3* centered at a lattice point
...4DQ3o3o4x, variation ofsidpith2.645751
qracorn5Dquasiretrocellirhombated penteract1.192297
qragishi (old: qraghi)4Dquasirhombated grand stellated hecatonicosachoron1.662508
qrasquit2Dquasirhombated square tiling
qrax6Dquasirhombatedhexeract0.819496
qrico4Dquasirhombated icositetrachoron1.082392
qrid3Dquasi rhombicosidodecahedron, great (non-convex) rhombicosidodecahedron (i.e.notgrid)0.716891
qridaquit gissidu4Dexpanded axially-great-icosahedral ursachoron, (qrid,quit gissid)-based ursulate1.020794
qriddip4Dquasi-rhombicosidodecahedron prism0.874032
qrigfix (old: querfix)4Dquasirhombated great faceted hexacosachoron1.027486
qrigogishi (old: qrahi)4Dquasirhombated great grand stellated hecatonicosachoron0.799575
qrit4Dquasirhombated tesseract0.765367
qro8Dquasirhombated octeract0.870264
qrothat2Dquasirhombitrihexagonal tiling
quacagorx6Dquasicelligreatorhombatedhexeract2.687345
quacant5Dquasicellated penteractitriacontiditeron1.021221
...4Dvertex figure ofquasicellated penteractitriacontiditeron1.118034
quacgarn5Dquasicelligreatorhombated penteract2.143163
quacox6Dquasicellihexeract1.042011
quacpot5Dquasicelliprismated triacontiditeron1.102028
quacrant5Dquasicellirhombipenteractitriacontiditeron1.192297
quactix6Dquasicellitruncatedhexeract1.431870
quad pagaxhi4Dquasidisprismatogrand hexacosihecatonicosachoron0.874032
quadippady4Dquasidisprismatodishecatonicosachoron, Unholey Terror1.414214
quafdidoh5Dquasifacetodecadishexadecateron1.620185
quapox6Dquasiprismatedhexeract0.937379
quappin5Dquasiprismatedpenteract0.914214
quarn5Dquasirhombatedpenteract0.792893
quawros4Dquadratic ({8} || cube-)wedge rosette, bridge cyclotetraaugmentedtesseract, ring-augmentedtesseract,cube || {8} ||cube, {4} ||squobcu || {4}
quaxoke8Dquasi-exiocteracti-diacosipentacontahexazetton1.338990
quequapech3Dquasiquasiprismated cubic honeycomb
querco3Dquasirhombicuboctahedron, great rhombicuboctahedron (butnotgirco)0.736813
quercoa quithu4D(querco,quith)-based ursachoron0.986869
quercope4Dquasirhombicuboctahedron prism0.890446
quersa7Dquasirhombated hepteract0.845261
queto8Dquasitruncated octeract0.741790
quicgrat (old: cogqrit)5Dquasicelligreat rhombated triacontiditeron, (celligreat quasirhombated triacontiditeron)2.001839
quicpatint5Dquasicelliprismatotruncated penteractitriacontiditeron1.949424
quidex4Dquatro-icositetradiminishedhexacosachoron, tristellatododecahedral enneacontahexachoron, dual ofsadi
quidpith (old: qippith)4Dquasi(dis)prismatotesseractihexadecachoron0.890446
quidpixhi4Dquasidisprismatohexacosihecatonicosachoron0.763932
quil7Dpentacosiheptacontihexa-pentacontihexa-exon,vertex figure ofyab0.866025
quipdohi4Dquasiprismatodishecatonicosachoron1.328131
quiphi4Dquasiprismatohecatonicosachoron0.726543
quiposaz7Dquasipetated hepteractihecatonicosoctaexon1.242133
quippic4Dquasiprismatotetracontoctachoron0.765367
quippirfix4Dquasiprismatorhombated faceted hexacosachoron3.531591
quippirgashi4Dquasiprismatorhombated grand stellated hecatonicosachoron1.348948
quippirgax4Dquasiprismatorhombated grand hexacosachoron1.021064
quippirghi4Dquasiprismatorhombated grand hecatonicosachoron2.400819
quipqrich3Dquasiprismated quasirhombated cubic honeycomb
quiprich3Dquasiprismatorhombated cubic honeycomb
quiprin5Dquasiprismatorhombated penteract1.488108
quiproh4Dquasiprismatorhombated hexadecachoron1.082392
quiptin5Dquasiprismatotruncated penteract1.416813
quishexah3Dhyperbolic quarter order 4hexagonal-tiling honeycomb0.816497i
quistet3Dquadratisnub tetratetrahedron, chiraledge facetingsidtid-0-8-12-0-b0.866025
quit gashi4Dquasitruncated grand stellated hecatonicosachoron0.953850
quit gishi4Dquasitruncated great stellated hecatonicosachoron0.953850
quit gissid3Dquasitruncated great stellated dodecahedron, great stellated truncated dodecahedron, great stellatruncated dodecahedron0.657550
quit gissiddip4Dquasitruncated-great-stellated-dodecahedron prism0.826058
quit gogishi4Dquasitruncated great grand stellated hecatonicosachoron0.677481
quit sishi4Dquasitruncated small stellated hecatonicosachoron2
quit sissid3Dquasitruncated small stellated dodecahedron, small stellated truncated dodecahedron, small stellatruncated dodecahedron0.852911
quit sissidagird4Dquit sissid atopgird0.874032
quit sissiddip4Dquasitruncated-small-stellated-dodecahedron prism, small-stellated-truncated-dodecahedron prism0.988665
quitar (old: quahri)3Dquasitruncated rhombihedron, quasihyperhombicosicosahedron,compound of 5quith0.579471
quitasa7Dquasitruncated hepteract0.712292
quitch3Dquasitruncated cubic honeycomb
quitco3Dquasitruncated cuboctahedron, great truncated cuboctahedron, stellatruncated cuboctahedron1.062393
quitcope4Dquasitruncated-cuboctahedron prism1.174172
quitdid3Dquasitruncated dodecadodecahedron, stellatruncated dodecadodecahedron1.658312
quitdiddip4Dquasitruncated-dodecadodecahedron prism1.732051
quiten9Dquasitruncated enneract0.770160
quith3Dquasitruncated hexahedron, stellated truncated hexahedron, stellatruncated cube0.579471
...4Dquith atop "squares ofthah", reducedquith atop2oct+6{4}0.739539
quithaquitco4Dquasitruncated hexahedron atopquasitruncated cuboctahedron1.082392
quithdow7D(bi-)quithic disphenoid, (bi-)quithic duopyramid,quith atop fully orthogonalquith0.646447
quithesc5Dquasitruncated-hexahedralscalene,quasitruncated-hexahedral-pyramid pyramid, line atop fully orthogonalquasitruncated hexahedron0.633157
quithip4Dquasitruncated-hexahedron prism0.765367
quithpy4Dquasitruncated-hexahedral pyramid0.613502
quitit4Dquasitruncated tesseract0.615370
quititip5Dquasitruncated-tesseract prism0.792893
quitothit2Dquasitruncated trihexagonal tiling
quitoxog6Dquasiteratedhexeractihexacontatetrapeton1.137055
quitsquat2Dquasitruncated square tiling
quittin5Dquasitruncated penteract0.649286
quoptax6Dquasiprismatotruncated hexeract1.686163
quotacog6Dquasitericellated hexacontatetrapeton1.121320
quothat2Dquasitruncated hexagonal tiling
quotox6Dquasitruncated hexeract0.681517

R

...3Drhombic enneacontahedron
rabird5Dretrobirhombidodecateron1.414214
raccoth5Dretrocellitriacontadiahexadecateron1.224745
...4Dvertex figure ofretrocellitriacontadiahexadecateron0.912871
rackix6Dretrocelliskewed hexeract1.581139
racoh3Dhyperbolic x3o4x3o4*a tesselation, rectified cubic-octahedral honeycomb1.045866i
racpix5Dretrocelliprismatedhexateron1.632993
racyxh5Drhombated cyclohexateric honeycomb, cyclorhombated hexateric honeycomb
rad (old: rhode)3Drhombic dodecahedron, granatahedron, Voronoi cell of face-centered cubic (fcc)lattice, terminally chamferedcube, terminally chamferedoctahedron, surtegmated cube, surtegmated octahedron,Waterman polyhedron number 4 wrt. primitive cubiclattice C3 centered at a lattice point,Waterman polyhedron number 2 (and 6) wrt. body-centered cubiclattice C3* centered at a lattice point
radah5Dretrodishexadecateron0.790569
...4Dvertex figure ofretrodishexadecateron0.774597
radatathi4Dretroditetrahedronary dishecatonicosachoron1.414214
raddirag6Drhombidodecahedraly-diminishedrectified hexacontatetrapeton1
rade10Drectified dekeract, rectified icosaxennon2.121320
raded3Drhombidodecadodecahedron1.322876
raded adoe4Draded atop3doe1.432173
raded adoe4Drhombidodecadodecahedron atopdodecahedron1.432173
...3Dedge facetingraded-1-10-5-51.322876
radeda tigid, raded || tigid4Drhombidodecadodecahedron atoptruncated great dodecahedron2.363565
radh3Drhombic dodecahedral honeycomb,Voronoi complex of face-centered cubic (fcc)lattice
radiddip (old: radedip)4Drhombidodecadodecahedron prism1.414214
rafficdi4Dretrofrustic tetracontoctadisicositetrachoron1.414214
raffixthi4Dretrofrustic hexacositrishecatonicosachoron2.236068
rag (old: ric)6Drectifiedhexacontitetrapeton,lattice B6 contact polytope (span of its small roots),lattice D6 contact polytope (span of its roots), equatorial cross-section ofgee-firstrez, equatorial cross-section of vertex-firstlaq1
ragabrag7Drag atopbrag,rag-firstrotunda ofbarz1.224745
ragaghi4Drectifiedgreat grand hecatonicosachoron1.070466
..., ragaghi || tigaghi5D(degenerate)ragaghi atoptigaghi∞   i.e. flat in euclidean space
ragashi4Drectifiedgrand stellated hecatonicosachoron1.175571
ragashia5Drectified grand stellated hecatonicosachoron alterprism1.248606
ragasochax7Drag atopsochax,rag-first cap ofranq1.414214
raggix4Drectifiedgrand hexacosachoron0.726543
raggixu5Draggix-based ursateron1.175984
raghi4Drectifiedgrand hecatonicosachoron1.902113
ragip7Drectified-hexacontitetrapeton prism1.118034
ragishi4Drectifiedgreat stellated hecatonicosachoron1.175571
rah3Drhombihexahedron,compound of 3cube0.866025
raheath3Dhyperbolic o3o3x7o tesselation, rectifiedheat honeycomb1.312710i
rahet3Dhyperbolic o3x3o7o tesselation, rectifiedorder 7 tetrahedral honeycomb0.657675i
rahi4Drectifiedhecatonicosachoron4.534568
..., rahi || tex5D(degenerate)rahi atoptex∞   i.e. flat in euclidean space
rahia sidpixhi5D(degenerate)rahi atopsidpixhi∞   i.e. flat in euclidean space
rahipe5Drectified-hecatonicosachoron prism4.562051
rahitte4Drectified hyperbolichecatoniicosachoric tetracomb2.910693i
rahrie3Drhombihyperhombicosicosahedron,compound of 5socco1.398966
rake10Drectified chilliaicositetraxennon,lattice B10 contact polytope (span of its small roots),lattice D10 contact polytope (span of its roots)1
raktatant5Dretroskewtrigonary trispenteractitriacontiditeron1.5
ram6Drectifiedpentacontitetrapeton,Gosset polypeton 02,2,1, Voronoi cell oflattice E6*, equatorial cross-section ofrojak-firstrolaq1.732051
ramoh6Drectified-pentacontitetrapetic hexacomb,Gosset hexacomb 02,2,2,Voronoi complex oflattice E6*
ranq7Drectified hecatonicosihexapentacosiheptacontihexaexon, equatorial cross-section oflaq-firstbay1.414214
rap (old: rip, alt.: tetaoct), tet || oct, K-4.54Drectifiedpentachoron, pyrorectichoron,tetrahedralcupola,vertex figure ofhin,tetrahedron atopoctahedron,Gosset polytope 02,10.774597
rapa penp6Drap atoppenp,rap-first cap ofril0.845154
rapaco (alt.: tetoct cotric)5Drap atopco, 0.176208-lune ofrat, (tet,oct,co)-trigonic,rap-firstlune ofrat1
rapadeca5Drap atopdeca,rap-first cap ofsirhin1.620185
rapalpenp6Drap atop invertedpenp,pen-first medial subsegment ofjak0.816497
rapalprip, rap || inv prip5D(degenerate)rap atop invertedprip∞   i.e. flat in euclidean space
rapalsrip5Drap atop invertedsrip,rap-first cap ofspix1.190238
rapaltip5D(degenerate)rap atop invertedtip∞   i.e. flat in euclidean space
rapaltrarap7Drectified-pentachoron atop alternate(triangle, rectified pentachoron)-duoprism0.968246
rapaspid5Drectified pentachoron atopsmall prismated decachoron,rap-first half ofrat1
rapasrip5Drectified pentachoron atopsmall rhombated pentachoron,rap-first cap ofnit1.224745
rapatip5Drap atoptip,rap-first cap ofsarx0.774597
rapatrapen7Drectified pentachoron atoptriangle-pentachoron duoprism,rap-first cap ofroc0.866025
rapatut (alt.: tetoct tuttric)5Drap atoptut, (tet,oct,tut)-trigonic1.190238
rapdafup9Drectified-pentachoronduoantifastegium1.118034
rapdip8Drectified-pentachoron duoprism1.095445
rapente4Drectified hyperbolic order 5pentachoric tetracomb1.272020i
rapepe8Drappeppene1
rapesc6Drectified-pentachoricscalene,rectified-pentachoron-pyramid pyramid, line atop fully orthogonalrectified pentachoron0.816497
rapescu3Dretrograde pentagonal cuploid, retrograde pentagonal semicupola0.866025
rapete7Draptettene0.866025
raphitte4Drectified hyperbolic order 5hecatonicosachoric tetracomb0.668740i
rapirx5Dretroprismatorhombated hexateron1.914854
rappaf (alt.: rapalrappip)6Drectified-pentachoralantifastegium,rectified pentachoron atop invertedrectified-pentachoral prism0.925820
rappip5Drectified-pentachoron prism,vertex figure ofrojak0.921954
rappippy6Drectified-pentachoron-prismatic pyramid, vertex pyramid ofrectified icosiheptaheptacontidipeton1.290994
rappisdi4Dretroantiprismatosnub disicositetrachoron1
...4Drappisdi+mesdi+288{4} (?)1
rappy5Drectified-pentachoric pyramid, vertex cap ofhin0.790569
rappyp6Drectified-pentachoron-pyramid prism0.935414
rapsady4Dretroantiprismatosnub dishecatonicosachoron1.618034
rapt5Drectified-pentachoric (line-)tegum,rectified-pentachoric dipyramid...
raptum5Drap-first bistratic cap ofthin,rap-basedtutsatope,rap-based tutism1.903943
rapu5Drectified-pentachoron-based ursateron,rap-basedursulate1.258489
raquahri3Drhombiquasihyperhombicosicosahedron,compound of 5gocco0.736813
rarsisresa2Drhombiretrosnub squarirhombisquariapeirogonal tiling
rasa (old: ras)7Drectified hepteract, equatorial cross-section ofroc-firstbro1.732051
rasdi4Dretrosnub icositetrachoron, retrosnub disicositetrachoron0.618034
rasher3Drhombisnub hyperhombihedron,compound of 5sroh1.398966
rasishi4Drectifiedsmall stellated hecatonicosachoron2.802517
rasishia5Drasishi alterprism2.829949
...5Drasishia + 2 2rasishi2.829949
rasisquat2Dretrosnub square tiling
rasquacu3Dretrograde square cupola, crossed square cupola, 4/3-cupola0.736813
rasquahr3Drhombisnub quasihyperrhombihedron,compound of 5groh0.736813
rasseri3Drhombisnub rhombicosicoahedron,compound of 5sirco1.398966
rassersa2Drhombisnub squarirhombisquariapeirogonal tiling
rassid3Drhombisnub dodecahedron,compound of 6dip1.693527
rastacu3Dretrograde pentagrammic cupola, 5/3-cupola0.716891
rat5Drectifiedtriacontiditeron, rectified pentacross,vertex figure ofhinoh,lattice B5 contact polytope (span of its small roots),lattice D5 contact polytope (span of its roots), equatorial cross-section oftac-firstrag, equatorial cross-section ofhin-firstmo1
ratahinnip7Drectified-triacontiditeron atopdemipenteract-prism1
ratanit6Drectified triacontaditeron atoppenteractitriacontiditeron,rat-firstrotunda ofbrag1.224745
ratasiphin6Drat atopsiphin,rat-first cap ofrojak1.290994
ratchet5Dretrotriacontidicellihemitriacontaditeron1
...4Dvertex figure ofretrotriacontidicellihemitriacontaditeron0.866025
rath3Dhyperbolic rectified (order 6)tetrahedral honeycomb1i
ratho4Drectified tesseractihemioctachoron1
rathotathibit4Drhombitrihexagonal-omnitruncated-trihexagonal duoprismatic tetracomb
ratip6Drectified-triacontiditeron prism1.118034
ratkus7Dretroteriskewed hepteract1.658312
ratricu3Dretrograde trigonal cupola, 3/2-cupola0.707107
ratu6Drat-based ursapeton1.738546
rawcax (old: rawvdipdopdix)5Dretrosphenary cellihexateron, (retrosphenoverted disprismatoduoprismatodiakishexateron)1.290994
...4Dvertex figure ofretrosphenary cellihexateron0.921954
rawcbinant5Dretrosphenary cellibiprismatopenteractipenteractitriacontaditeron2.660531
rawn (old: rawvanant)5Dretrosphenary penteract2.207107
rawt5Dretrosphenary triacontaditeron1.732051
rawvathi4Dretrosphenoverted triakishecatonicosachoron2.689994
rawvatoth4Dretrosphenoverted tesseractitesseractihexadacachoron1.847759
rawvaty4Dretrosphenoverted triakisicositetrachoron2.613126
rawvax6Dretrosphenary hexeract2.515637
rawvhiddix4Dretrosphenoverted hecatonicosadishexacosachoron1.258409
rawvhitto4Dretrosphenoverted hexadecatesseractioctachoron1.732051
rawvid tixady4Dretrosphenoverted ditrigonary hexacosadishecatonicosachoron5.330704
rawvo8Dretrosphenary octeract3.040171
rawvsa7Dretrosphenary hepteract2.790257
rawvtip4Dretrosphenoverted triakispentachoron1.183216
rawx5Dretrosphenary hexateron1.290994
rax6Drectifiedhexeract, rectified dodecapeton, equatorial cross-section ofbrox-firstbersa1.581139
raxh6Drectified hexeractic pentacomb
rebatch3Drectifiedbitruncated cubic honeycomb
recaptid5Dretrocelliprismatotruncated dodecateron2.236068
recard5Dretrocellirhombated dodecaateron1.658312
recarnit5Dretrocellirhombated penteractitriacontaditeron2.660531
reco3Drectifiedcuboctahedron, variation ofsmall rhombicuboctahedron,Waterman polyhedron number 6 wrt. primitive cubiclattice C3 centered at a lattice point,Waterman polyhedron number 3 wrt. face-centered cubiclattice A3 centered at a lattice point1.732051
recont4Drectifiedtetracontoctachoron6.754807
...4DrectifiedShephard's hexadecachoron,complex polychoronop-4-o2-3-x2-3-o2
...4DrectifiedWitting polychoron,complex polychorono3-3-x3-3-o3-3-o3
...3Dcomplex polyhedrono3-3-x3-4-o2,complex polyhedronx3-3-o3-3-x3
...2Dcomplex honeycombo3-3-x3-4-o3
...3DShephard's3-generalised cuboctahedron,complex polyhedrono3-4-x2-3-o2
...2Dcomplex honeycombo4-3-x4-4-o2
...3DShephard's4-generalised cuboctahedron,complex polyhedrono4-4-x2-3-o2
...3DShephard's5-generalised cuboctahedron,complex polyhedrono5-4-x2-3-o2
...5Drectification/ambification oficoap1.847759
...4Drectifiedhyperbolic o4x4o3*a4x4o3*a tetracomb...
...3DShephard'sp-generalised cuboctahedron,complex polyhedronop-4-x2-3-o2
...4DrectifiedShephard's tesseract,complex polychoronop-4-x2-3-o2-3-o2
...2Dcomplex honeycombop-4-x2-4-o2,complex honeycombx2-4-op-4-x2
...2Dcomplex honeycombop-4-x2-4-or
...3Drectifiedhyperbolic x4o3o4x4*b tesselation...
recta3Drectangular alterprism, rectangular trapezoprismsqrt[c2+(a+b)2/2]/2
recto8Drectified octeract, rectified hexadecazetton, equatorial cross-section ofrene-firstbarn1.870829
recytatoh (old: rebtatoh)3Drectifiedcyclotruncated tetrahedral-octahedral honeycomb (rectifiedbitruncated tetrahedral-octahedral honeycomb)
...4Dreduced 3/2-antifastegium, triangular pucloidfastegium, {3} || pseudo gyratedtrip0.774597
reday9Drectified decayotton,vertex figure ofhede,Gosset polytope 07,10.894427
redeca4Drectifieddecachoron2.828427
redscox (alt.: trisoo)6Dhecatonenenecontadia-diminishedsmall cellihexeract, partially triexpandedxedrag, tri - (4,8,8)-trioprism1.978437
...3D(degenerate) reduceddid atopid
...4Dreduced( ofx3/2oxx3ooo&xt by 2tet )0.874032
...4Dreduced( ofx3/2oxx3xxx&xt by 4x {6/2} )1.136572
...4Dreduced( ofx3/2oxx4ooo&xt by oct+6{4} )0.899454
...4Dcuboctahedral retro-cuploid1
regikaike4Drectifiedgikaike1.732051
rek8Drectified diacosipentacontahexazetton,lattice B8 contact polytope (span of its small roots),lattice D8 contact polytope (span of its roots), equatorial cross-section ofek-firstriv1
ren9Drectified enneract, rectified octadecayotton, equatorial cross-section ofreday-firstbrade2
rene8Drectified enneazetton,vertex figure ofhenne,Gosset polytope 06,10.881917
renepy9Drectified-enneazettonal pyramid, vertex pyramid ofdemienneract1.060660
repenp (alt.: ampenp)5Drectified/ambifiedpenp1.264911
repip (alt. ampip)3Drectified/ambifiedpip,o2o5o symmetricco relative1.203002
repirt5Dretroprismatorhombated triacontiditeron3
repuko8Dretropetiskewed octeract1.732051
rerahi4Do3x3o5f, rectifiedrectified-hecatonicosachoron, variation ofsrahi9.013835
rerax6Drectifiedrectified-hexeract, variation ofsmall rhombated hexeract2.645751
rerich3Drectifiedrectified-cubic-honeycomb, variation ofsmall-rhombated-cubic-honeycomb
rerico4Dx3o4q3o, rectifiedrectified-icositetrachoron, variation ofsmall rhombated icositetrachoron3.316625
rerin5Drectifiedrectified-penteract2.645751
rerit4Do3x3o4q, rectifiedrectified-tesseract, variation ofsrit2.236068
rescad5Drectifiedscad1.732051
resibrid5Drectifiedsibrid2.645751
residpith (alt.: amsidpith)4Drectified/ambifiedsmall-disprismated-tesseractihexadecachoron2.797933
residpixhi (alt.: amsidpixhi)4Drectified/ambifiedsmall-disprismated-hexacosihecatonicosachoron10.424281
resirco (alt.: amsirco)3Drectified/ambifiedsmall-rhombated-cuboctahedron2.613126
respic4Drectifiedsmall prismated tetracontoctachoron3.557647
respid4Drectifiedsmall prismated decachoron1.732051
resrid (alt.: amsrid)3Drectified/ambifiedsmall-rhombated-icosidodecahedron4.352502
resrip (alt.: amsrip)4Drectified/ambifiedsrip2.144761
restaf6Drectifiedstaf1.732051
retah (alt.: amtah)4Drectified/ambifiedtesseractihexadecachoron4.123106
retdip (old: retriddip)4Drectifiedtriddip1.290994
retepe (alt.: amtepe)4Drectified/ambifiedtepe1.224745
rethat2Drectifiedtrihexagonal-tiling, variation ofsmall-rhombitrihexagonal-tiling
reti (alt.: amti)3Drectified/ambifiedtruncated icosahedron4.854102
retic (alt.: amtic)3Drectified/ambifiedtruncated cube3.414214
retid (alt.: amtid)3Drectified/ambifiedtruncated dodecahedron5.854102
retisdip (alt.: amtisdip)4Drectified/ambifiedtisdip1.527525
retoe (alt.: amtoe)3Drectified/ambifiedtruncated octahedron2.121320
retrat2Dretroelongated trangular tiling
retratet (alt.: amtratet)5Drectified/ambifiedtratet1.354006
...3Dblend ofretro-elongated triangular-tiling prisms
retrip (alt.: amtrip)3Drectified/ambifiedtrip, Lich's nemesis, kernel oftrip andm m3o,o2o3o symmetricco relative0.816497
rettidjak6Drectification oftridiminished icosiheptaheptacontidipeton1.632993
retut (alt.: amtut)3Drectified/ambifiedtruncated tetrahedron2.121320
rexhi (alt.: amxhi)4Drectified/ambifiedhexacosihecatonicosachoron15.126249
rez (old: rhio)7Drectified hecatonicosoctaexon,lattice B7 contact polytope (span of its small roots),lattice D7 contact polytope (span of its roots), equatorial cross-section ofzee-firstfy, equatorial cross-section ofzee-firstrek1
rhohid5Drectifiedhexadecahemidecateron1
rhom3Drhombihedron,compound of 5cube0.866025
...4D(small) rhombatedgeneralized Shephard hexadecachoron,complex polychoronx2-3-o2-3-x2-4-op
...4D(small) rhombatedWitting polychoron,complex polychoronx3-3-o3-3-x3-3-o3
...3Dcomplex polyhedronx3-3-o3-4-x2
...3Dcomplex polyhedronxp-4-o2-3-x2
...4D(small) rhombatedgeneralized Shephard tesseract,complex polychoronxp-4-o2-3-x2-3-o2
...3Dcomplex polyhedronxp-4-o2-4-x2
...3Dcomplex polyhedronxp-4-o2-4-xr
...2Dpartially contractedhexagonal tiling, rhombic uBxx3uxBx3xooA3*a&#zx
...2Dpartially expandedtri-hexagonal rhombic tiling, rhombic uBxx3xoAo3xooA3*a&#zx
...2Dtri-hexagonal rhombic tiling
...2Dmultiform rhombic tiling with {5}, {10/3}, and {∞}
rhote (old: rattic)3Drhombic triacontahedron, terminally chamfereddodecahedron, terminally chamferedicosahedron, surtegmated dodecahedron, surtegmated icosahedron
ri3Drhombicosahedron1.322876
...3Dri+12{10/2}1.322876
...3Dri+12{10/4} (?)1.322876
ribfoh8Drectified diacositetracont-dischiliahectohexaconta-zettic octacomb,Gosset heptacomb 05,2,1
ribrant5Dretrobirhombipenteractitriacontaditeron2.236068
ricasrit, rico || srit5Drectified-icositetrachoron atopsmall-rhombated-tesseract1.847759
ricatah5Drico atoptah,rico-first cap ofsibrant2.236068
rich3Drectified cubic honeycomb
rico4Drectifiedicosatetrachoron, cantellatedhexadecachoron,hexadecachoron-derived Gévay polychoron, equatorial cross-section ofico-firstsart1.732051
...4Drico-cap augmentedthex-rotunda...
..., rico || gyro srico5D(degenerate)rico atop gyratedsrico∞   i.e. flat in euclidean space
..., rico || proh5D(degenerate)rico atopproh∞   i.e. flat in euclidean space
ricoa (old: ricoalrico), rico || gyro rico5Drectified icositetrachoron alterprism,rectified icositetrachoron atop gyratedrectified icositetrachoron1.778824
ricoa ticotum5Drico-basedtutsatope,rico-based tutism,rico-first bistratic cap ofpattit2.738613
ricoasadi5Drico atopsadi1.738546
ricoaspic5Drectified icositetrachoron atopsmall prismated icositetrachoron1.847759
ricoatico5D(degenerate)rico atoptico∞   i.e. flat in euclidean space
ricope5Drectified-icositetrachoron prism1.802776
ricot4Drectified icositetrachoric tetracomb
rid3Drectifiedicosidodecahedron, variation ofsmall rhombicosidodecahedron3.077684
ridatathi4Dretroinverted ditetrahedral triakishecatonicosachoron1.414214
ridatha3Drectified ditetratihemiapeiratic honeycomb
ridditdy4Dretroditrigonary dishecatonicosachoron1.732051
riddoh3Dhyperbolic rectified order 4 dodecahedral honeycomb1.272020i
ridhi4Dretroinverted dishecatonicosachoron1.902113
ridimex (alt.: idimrox)4Drectifiedicosidiminished hexacosachoron, icosidiminishedrectified hexacosachoron3.077684
ridtidohi4Drectified ditrigonary dishecatonicosachoron1.732051
riffy8Drectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t1(41,2)1.732051
rigfix4Drectifiedgreat faceted hexacosichoron0.726543
..., rigfix || quipdohi5D(degenerate)rigfix atopquipdohi∞   i.e. flat in euclidean space
..., rigfix || sirgaghi5D(degenerate)rigfix atopsirgaghi∞   i.e. flat in euclidean space
riggidtixhi4Drectified great ditrigonary hexacosihecatonicosachoron1.732051
righi4Drectifiedgreat hecatonicosachoron1.902113
righia5Drectified great hecatonicosachoron alterprism1.917564
rigogishi4Drectifiedgreat grand stellated hecatonicosachoron0.661585
rigoh8DrectifiedGosset octacomb 52,1
rigytoh3Drectified/ambifiedgyrated tetrahedral-octahedral honeycomb
rih3Dhyperbolic rectified order 3icosahedral honeycomb1.427535i
rihach3Dhyperbolic rectified order 6cubic honeycomb0.707107i
rihexah3Dhyperbolic rectified (order 3)hexagonal-tiling honeycomb1.732051i
rihihexah3Dhyperbolic rectified order 6hexagonal-tiling honeycomb0.577350i
rihix4Dretroinverted hecatonicosihexacosachoron1.175571
ril (old: riss)6Drectifiedheptapeton,vertex figure ofhesa,Gosset polytope 04,10.845154
rila (old: rilalril)7Drectified heptapeton alterprism,rectified heptapeton atop invertedrectified heptapeton,hop-first medial segment ofnaq0.866025
rilalbril7Drectified heptapeton atop invertedbirectified heptapeton, equatorial monostratic segment ofdemihepteract0.935414
rilastaf7Dril atopstaf,ril-firstrotunda ofrez1
rillip7Drectified-heptapeton prism,vertex figure ofrobay0.981981
rilpy7Drectified-heptapetonal pyramid, vertex pyramid ofdemihepteract0.935414
rin5Drectifiedpenteract, equatorial cross-section ofnit-firstbrox1.414214
rinah5Dretropenteractihexadecateron0.790569
...4Dvertex figure ofretropenteractihexadecateron0.774597
rinathin6Drectified penteract atoptruncated demipenteract,rectified demipenteract-first cap ofdemirectified icosiheptaheptacontidipeton2.160247
rinhit5Dretropenteractihemitriacontiditeron1
rinnip6Drectified-penteract prism1.5
rinoh5Drectified penteractic pentacomb
rinquoh7Drectified hecatonicosihexapentacosiheptacontihexaexic honeycomb
ripahi4Dretroinverted prismatohecatonicosachoron4.534568
...4Dripahi+600 2thah (?)4.534568
ripdip4Drhombiprismato dispentachoron1.612452
ripech3Dhyperbolic rectified order 5 cubic honeycomb1.057371i
ripped3Dhyperbolic rectified order 5 dodecahedral honeycomb0.813126i
ripperhin5Dretroprismatorhombidemipenteract2.150581
rippix5Dretroprismated hexateron1.190238
ript5Dretoprismated triacontiditeron1.870829
ripthin5Dretroprismatotruncatodemipenteract2.371708
risadi (alt.: idrox)4Drectifiedsnub icositetrachoron, icositetradiminishedrectified hexacosachoron3.077684
risadit4Drectified/ambifiedsnub icositetrachoric tetracomb
risdoh3Drhombisnub dishexahedron,compound of 6cube, Skilling's compound0.866025
rishexah3Dhyperbolic rectified order 4hexagonal-tiling honeycomb1i
risquah3Dhyperbolic rectifiedsquare-tiling honeycomb1.224745i
rissidtixhi4Drectified small ditrigonary hexacosihecatonicosachoron1.732051
rit4Drectifiedtesseract, rectified octachoron, birectifiedhexadecachoron, runcic tesseract, equatorial cross-section ofico-firstnit1.224745
..., rit || tat5D(degenerate)rit atoptat∞   i.e. flat in euclidean space
rita (old: ritag rit)5Drit atop gyrorit, medial segment ofhex-firstsiphin1.274755
rita sidpith, rit || sidpith5Drectified-tesseract atopsmall-disprismated-tesseractihexadecachoron1.502958
ritag thex5Drit atop gyratedthex,rit-first cap ofsirhin1.620185
ritahin6Drit atophin, (rit,+gyrohex, -gyrohex)-trigonic1.290994
ritarico5Drectified-tesseract atoprectified-icositetrachoron,rectified-tesseract-first segment ofsmall-prismated-triacontiditeron1.870829
ritas6Dritaltersquarism, cyclotetra-diminishedsochax, medial segment ofsiphina, partialStott expansion ofhax1.322876
ritasrit, rit || srit5Drectified-tesseract atopsmall-rhombated-tesseract2.632865
ritatah, rit || tah5D(degenerate)rit atoptah∞   i.e. flat in euclidean space
ritathex5D(degenerate)rit atopthex∞   i.e. flat in euclidean space
ritathexu5Drit-based ursateron1.627127
ritch3Dhyperbolic x3o3x3o4*a tesselation, rectified tetrahedral-cubic honeycomb1.429970i
ritdip8Drectified-tesseractic duoprism1.732051
rite (alt.: ikaidbicu)4Drectifiedite,ikaid bicupola...
ritgyco7Drectified-tesseracticgyro-cuboctahedronism1.414214
ritgyo7Drectified-tesseractgyro-octahedronism, 384-diminishedpentacontihexahecatonicosihexaexon1.322876
ritgyt6Drectified-tesseracticgyrotrigonism1.290994
rithsithbit4Drhombitrihexagonal-simotrihexagonal duoprismatic tetracomb
ritrah3Dhyperbolic rectifiedtriangular-tiling honeycomb1i
rittip5Drectified-tesseract prism1.322876
rittit4Drectified tesseractic tetracomb, quartertesseractic tetracomb
riv9Drectified pentacosidodecayotton,lattice B9 contact polytope (span of its small roots),lattice D9 contact polytope (span of its roots), equatorial cross-section ofvee-firstrake1
rix5Drectifiedhexateron,vertex figure ofhax,Gosset polytope 03,1, equatorial cross-section ofhix-firstjak0.816497
rixa (alt.: pabdihax, old: rixalrix)6Drectified hexateron alterprism, parabidiminisheddemihexeract,rectified hexateron atop invertedrectified hexateron0.866025
rixaf7Drectified-hexateron antifastegium,rix atop invertedrixip1
rixahixip7Drectified hexateron atophexateron prism,rix-first cap ofroc0.866025
rixalspix6Drectified hexateron atopsmall prismated hexateron,rix-first cap ofscal1.195229
rixap7Drectified-hexateron-alterprism prism,rixip atop invertedrixip1
rixasarx6Drectified hexateron atopsmall rhombated hexateron,rix-first cap ofbrox1.414214
rixasc7Drectified-hexateronalscalene,rectified-hexateronal-pyramid pyramid, line atop fully orthogonalrectified-hexateron1
rixascad6Drectified hexateron atopsmall cellated dodecateron, half ofrectified hexacontitetrapeton (itsrix-firstrotunda)1
rixaspix6Drectified hexateron atopsmall prismated hexateron,rix-first cap ofrojak1.290994
rixatix6Drix atoptix1.362770
rixhi4Dretroinverted hexacosahecatonicosachoron3.077684
rixip6Drectified-hexateron prism,vertex figure ofrolaq0.957427
rixpy6Drectified-hexateronal pyramid, vertex pyramid ofdemihexeract0.866025
rixu6Drix-based ursapeton1.335149
ro3D(chiral) rhombioctahedron,compound of 4trip0.763763
robay8Drectified diacositetracont-myriaheptachiliadiacosioctaconta-zetton, t1(21,4)2.645751
robyah8Drectified diacositetracont-myriaheptachiliadiacosioctaconta-zettic octacomb, heptacomb t1(25,1)
roc7Drectified octaexon,vertex figure ofhocto,Gosset polytope 05,10.866025
roca8D(degenerate)rectified octaexonalterprism∞   i.e. flat in euclidean space
rocalbroc8Droc atop invertedbroc,oca-first subsegment offy1
rocasuph8Droc atopsuph1
rocgrax5Dretrocelligreat rhombated hexateron2.327373
rocip8Drectified-octaexon prism,vertex figure ofrobyah1
rocpy8Drectified-octaexonal pyramid, vertex pyramid ofdemiocteract1
rocrax (old: sircrax)5D(small) retrocellirhombated hexateron1.658312
rofix4Drectifiedfaceted hexacosichoron3.077684
..., rofix || sirsashi5D(degenerate)rofix atopsirsashi∞   i.e. flat in euclidean space
rojak6Drectifiedicosiheptaheptacontidipeton1.290994
rojaka (alt.: pabdilin, old: rojakalrojak)7Drojak alterprism, parabidiminishedlin,rojak atop alternaterojak1.322876
rojaka hejak7Drojak atophejak,rojak-first cap ofrolaq1.732051
rojakaf8Drectified-icosiheptaheptacontidipeton alterfastegium,rectified-icosiheptaheptacontidipeton atop invertedrectified-icosiheptaheptacontidipetal prism1.414214
rojakap8Drojaka prism,rojakip alterprism1.414214
rojakatrim7Drojak atoptrim,jak-first subsegment ofranq1.414214
rojakip7Drectified-icosiheptaheptacontidipeton prism1.384437
rojaku7Drojak-based ursaexon2.847628
rojkoh6Drectifiedicosiheptaheptacontidipetic hexacomb
rolaq7Drectified pentacontihexapentacosiheptacontihexaexon1.732051
ropith (old: kroptit)5Dretroprismatotruncated hexadecateron2.738613
roptit5Dretoprismatotruncated triacontiditeron2.738613
roptix5Dretroprismatotruncatedhexateron1.848423
rorisassa2Drhombiretrosnub squarisquariapeirogonal tiling
rorpdah5Dretroretroprismated dishexadecateron1.870829
rosaqri (old: rasquahpri)3Drhombisnub quasirhombicosicosahedron, rhombisnub quasihyperpseudorhombicosicosahedron,compound of 5querco0.736813
rosassa2Drhombisnub squarisquariapeirogonal tiling
rosi3Drhombisnub icosahedron,compound of 10hip1.118034
...4Dvertex-firstrotunda ofhexacosachoron1.618034
rox4Drectifiedhexacosachoron3.077684
...4Drox+720pip (?)3.077684
roxahi, rox || hi5D(degenerate)rox atophi∞   i.e. flat in euclidean space
roxip5Drectified-hexacosachoron prism3.118034
ru10Drectified hendecaxennon, rectified undecaxennon,Gosset polytope 08,10.904534
rusch3Druncicantic snub cubic honeycomb

S

...5Dtetrahedral - n-prismantiprismoid...
...5Dtetrahedral - 2n-prismantiprismoid...
...4Ds-2N-x-2-x-M-o, M-prism-alternated4N-gon - M-gon duoprism...
...4Ds2x2s4x, square-alternatedsodip...
...3Dβ3/2o3β (?)...
...3Dβ3/2β3x3*a (?)...
...4Dβ3o3o4β (?)...
...4Dβ3o3o5β (?)...
...4Dβ3o3β3o (?)...
...4Dβ3o3β4β (?)...
...4Dβ3o3β4x (?)...
...4Dβ3o3β5o (?)...
...4Dβ3o3β5β (?)...
...4Dβ3o3β5x (?)...
...4Dβ3o4o3β (?)...
...3Dβ3o4β (?)1.398966
...4Dβ3o4β3o (?)...
...3Dβ3o5β (?)2.232951
...4Dβ3β3o3β (?)...
...4Dβ3β3o4β (?)...
...4Dβ3β3o5β (?)...
...4Dβ3β3β3o (?)...
...4Dβ3β3β3x (?)...
...4Dβ3β3β5o (?)...
...4Dβ3β3β5x (?)...
...2Dhyperbolic snub tiling of family o3o3o∞*a
...4Dβ3β3x3β (?)...
...4Dβ3β3x4β (?)...
...4Dβ3β3x5β (?)...
...4Dβ3β3x *b3o (?)...
...4Ds3s4o3o, mere hemiation oftruncated icositetrachoron, snub rhombatohexadecachoron2.645751
...6Dhyperbolic s3s4o3o3o4o pentacomb1.111786i
...4Dalternated truncated hyperbolic order 4 icositetrachoral tetracomb
...5Dhyperbolic s3s4o3o4o3o pentacomb0.351578i
...4Dβ3β4o3β (?)...
...3Dhyperbolic s3s4o4o tesselation...
...3Dhyperbolic s3s4o4x tesselation...
...4Dβ3β4β3o (?)...
...4Dβ3β4β3x (?)...
...2Dhyperbolic snub tiling of family o3o4o5*a
...4Dβ3β4x3β (?)...
...3Dβ3β5o3o (?)...
...4Dshi+120x 2sissid(?)...
...4Dprishi+120x 2did (?)...
...3Dβ3x3o1.172604
...4Dβ3x3o4β (?)...
...4Dβ3x3o5β (?)...
...4Dβ3x3β3o (?)...
...4Dβ3x3β3x (?)...
...4Dβ3x3β4β (?)...
...4Dβ3x3β4x (?)...
...4Dβ3x3β5o (?)...
...4Dβ3x3β5β (?)...
...4Dβ3x3β5x (?)...
...4Dβ3x3x3β (?)...
...4Dβ3x3x4β (?)...
...4Dβ3x3x5β (?)...
...3Dβ3x4β (?)2.317611
...4Dβ3x4β3o (?)...
...4Dβ3x4β3x (?)...
...4Dβ3x4x3β (?)...
...3Dβ3x5β (?)3.802395
...4Dhyperbolic s4o3o4s4*b tesselation0.353553i
...3Dhyperbolic alternated small prismated order-4square tiling honeycomb0.594604i
...3Dhyperbolics4o4o4s +x4x4o4o4*a blend tesselation0.594604i
...3Dhyperbolic o3o4s4o tesselation0.866025i
...3Dfamily of (generally hyperbolic) s4oPo4s tesselation
...5Dtetrahedral - square-prismantiprismoid...
...4Ds4x2s4x (?)...
...4Ds4x2x3o,trip-alternatedtodip...
...5Ds4x2x3o4s,trip-alternatedosirco1.914214
...3Dβ5/2o5β (?)...
...3Dβ5/2x5β (?)...
...3Dhyperbolic s5s3s5s honeycomb, alternated hyperbolic great prismatodisdodecahedral honeycomb
...3Ds60-r60-p12-h30
...5Dtriangular,tetrahedral duoantiprism...
...5Dtetrahedral - hexagon-prismantiprismoid...
sabach7Dsmall bicellatedhexadecaexon, bistericatedoctaexon1.414214
sabbadipady4Dsmall blendic disprismatodishecatonicosachoron2
sabbathi4Dsmall blendic trishecatonicosachoron2
saberjakh6Dsmall birhombatedicosiheptaheptacontidipetic hexacomb
sabippady (old: sabbippady)4Dsmall blendic prismatodishecatonicosachoron2
sabirch3Dsmall birhombatocubic honeycomb
saborx6Dsmall birhombatedhexeract, bicantellated hexeract2.645751
sabranq7Dsmall birhombated hecatonicosihexapentacosiheptacontihexaexon3.741657
sabred4Dsmall birhombatodecachoronsqrt[(2a2+2ab+3b2)/5]
sabric4Dsmall birhombatotetracontoctachoronsqrt[a2 + 2 sqrt(2) ab + 3b2]
sabril6Dsmall birhombatedheptapeton, bicantellated heptapeton1.558387
sabrila7Dsabril alterprism,sabril atop alternatesabril1.581139
sabrim (old: pirm, sirmak, skorm)6Dsmall birhombatedpentacontitetrapeton, (prismatorectified pentacontitetrapeton, small rhombated pentacontitetraheptacontidipeton, small heptacontidirhombated pentacontitetrapeton)3
sabro7Dsmall birhombated octaexon, bicantellated octaexon1.658312
sad phiddix4Dsmall dipentary hecatonicosadishexacosachoron2.497212
saddid3Dsmall dodekicosidodecahedron2.232951
saddiddip4Dsmall-dodekicosidodecahedron prism2.288246
sadencorn (old: dancrin)5Dsmall dispinocellirhombated penteract2.660531
sadi   (alt.: idex)4Dsnubicositetrachoron, snub disicositetrachoron, semistruncated icositetrachoron, icositetradiminishedhexacosachoron, snub rhombatohexadecachoron1.618034
sadiap5Dsnub disicositetrachoric antiprism, triangle-alternation oftruncated icositetrachoric prism2.692582
sadinnert5Dsmall dispenteractirhombated triacontaditeron2.010695
sadip5Dsnub-icositetrachoron prism, snub-disicositetrachoron prism, semistruncated-icositetrachoron prism1.693527
sadit4Dsnub icositetrachoric tetracomb, Gosset's non-Wythoffian tetracomb
sadixady4Dsmall dishexacosadishecatonicosachoron1.773668
sadixhix (old: sixhix)4Dsmall dodecahedronary hexacosahemihexacosachoron,compound of 25ihi (butnotgadixhix)1
sadlaq7Dhepteract-diminishedpentacontihexapentacosiheptacontihexaexon1
sadsadox4Dsmall disnub dihexacosachoron3.077684
sadsid3Dsmall disnub dodecahedron,compound of 12stap0.656431
sadtap4Dsmall ditetrahedronary prismatochoron,compound of 36dedip2.288246
sadtef pixady4Dsmall ditetrahedronary exofissary prismatohexacosadishecatonicosachoron2.288246
sadticaxady4Dsmall ditetrahedronary cubihexacosidishecatonicosachoron2.288246
sadtifady4Dsmall ditetrahedronarofissary dishecatonicosachoron2.288246
safthi4Dgreat retrofrustary trishecatonicosachoron2.236068
...3Dvertex figure ofsmall antifrustary trishecatonicosachoron0.816497
sanbathi4Dsmall spinoblendic trishecatonicosachoron2
sanbippady4Dsmall spinoblendic prismatodishecatonicosachoron2
sand tathi4Dsmall intercepted ditetrahedronary trishecatonicosachoron2.288246
sapisseri3D(chiral) snub pseudosnub rhombicosahedron,compound of 20thah0.707107
saquid paxhi4Dsmall quasidisprismatohexacosihecatonicosachoron, Holey Terror2.288246
saro7Dsmall rhombated octaexon, cantellated octaexon1.414214
sart5Dsmall rhombatedtriacontiditeron, cantellated pentacross, equatorial cross-section ofnit-firstram1.732051
sartabittit6Dsmall rhombated triacontadipeton atopbitruncated triacontadipeton,sart-first cap ofsmall birhombated hexacontitetrapeton2.236068
sarx5Dsmall rhombatedhexateron, cantellated hexateron1.290994
sarxa gippixtum6Dsarx-first bistratic cap ofshorjak,sarx-basedtutsatope,sarx-based tutism3.265986
sarxasibrid6Dsmall rhombated hexateron atopsmall birhombated dodecateron,rix-first subsegment ofbrox1.414214
sarxip6Dsmall-rhombated-hexateron prism1.384437
sarz7Dsmall rhombated hecatonicosoctaexon, cantellated heptacross1.732051
sassid3D(chiral) small snub dodecahedron,compound of 6stap0.656431
sassiph3Dsnub square-tiling prismatic honeycomb
satpeb8Dsmall triprismated bi-enneazetton, triruncinated enneazetton1.732051
satsa2Dsquariapeirotruncated squariapeirogonal tiling
saxoke8Dsmall exiocteracti-diacosipentacontahexazetton, heptellated octeract1.790840
sazazat2Dhyperbolic snub di-horocyclic tiling, snub apeirogonal tiling
sazdideta4Dsquare antitrapezary disicositetratidistesseratiapeiratic tetracomb
scad (old: shad)5Dsmall cellateddodecateron, small hedrated dodecateron, stericatedhexateron, expanded hexateron,vertex figure ofcyxh,lattice A5 contact polytope (span of its roots), equatorial cross-section ofhix-firststaf, equatorial cross-section ofrix-firstrag, equatorial cross-section of vertex-firstmo1
scadaspix6Dsmall cellated dodecateron atopsmall prismated hexateron,scad-first cap ofscal1.195229
scadip6Dsmall-cellated-dodecateric prism1.118034
scadnicat5Dsmall cellidispenteracticellitriacontaditeron2.379961
scadupthix4Dsmall capped dipentary tetrishecatonicosahexacosichoron2.497212
scag6Dsmall cellihexacontitetrapeton, stericated hexacross2
scajakh6Dsmall celliicosiheptaheptacontidipetic hexacomb
scal6Dsmall cellatedheptapeton, stericated heptapeton1.195229
scala (old: scalal scal)7Dsmall cellated heptapeton alterprism,small cellated heptapeton atop invertedsmall cellated heptapeton, medial segment ofbarz1.224745
scala spil7Dscal atopspil1.322876
scalq7Dsmall cellatedpentacontihexapentacosiheptacontihexaexon2.236068
scant5Dsmall cellatedpenteractitriacontiditeron, stericatedpenteract, stericatedpentacross1.567516
scatnit5Dsmall cellitrispenteractitriacontaditeron2.379961
scicot4Dsmall cellated icositetrachoric tetracomb, small cellated demitesseractic tetracomb, stericated icositetrachoric tetracomb
sco7Dsmall cellated octaexon, stericated octaexon1.322876
scox6Dsmall cellihexeract, stericated hexeract1.978437
scuffi, ike-7-33Dsemicupolaically facetedicosahedron0.951057
scufgi, sissid-3-73Dsemicupolaically facetedgreat icosahedron0.587785
scyropot4Dsmall cyclorhombated pentachoric tetrachomb, small prismatodispentachoric tetracomb, cantellated pentachoric tetrachomb
se3Dsmall icosiicosahedron,compound of 5oct0.707107
sedit pathi4Dsmall exoditetrahedronary prismatotriakishecatonicosachoron2.288246
...4Dhyperbolic honeycomb with seed point at edge of right-angledoctahedron domain
...3Dhyperbolic honeycomb with seed point at face of right-angledoctahedron domain
seedatepthi4Dsmall exoditetrahedrary prismatotrishecatonicosachoron1.414214
sefdit dixdy4Dsmall exofissary ditrigonal dihexacosadihecatonicosachoron1.732051
sefidtethi4Dsmall exofissary ditetrahedronary tetrakishecatonicosachoron2.288246
sefradit thix4Dsmall exofissary retroditetrahedronary triakishecatonicosihexacosachoron2.288246
seihid3Dsmall icosihemidodecahedron1.618034
serch3Dsnub rectified cubic honeycomb
sersa7Dsmall rhombated hepteract, cantellated hepteract2.790257
seside3Dsmall snub icosicosidodecahedron, snub disicosidodecahedron, holosnub icosahedron, hastur1.458190
sesidip4Dsmall-snub-icosicosidodecahedron prism1.541531
sethalq7Dsmall terademifiedpentacontihexapentacosiheptacontihexaexon2.828427
setho4Dsesquitesseractihemioctachoron0.707107
setitdin5Dsmall tesseractitriacontidiadispenteract2.423081
seto7Dsmall terated octaexon, pentellated octaexon1.198958
setut4Dsmall tristetracosioctacontachoron1
...3Dvertex figure ofsetut0.866025
sez (old: shio)7Dhepteractihecatonicosoctaexon, equatorial cross-section ofbarz-firsttark1.414214
sgysrahi4Dswirl-gyratedsmall rhombated hecatonicosachoron, swirl-gyrated cantellated hecatonicosachoron6.735034
sha2Dsquare hemiapeirogonal tesselation, alternate square tiling
shadow5Dsmall heptagrammic disphenoid, small heptagrammic duopyramid, small heptagramm atop fully orthogonal small heptagramm0.674163
shafipto4Dsmall hexadecafaceted prismatotesseractioctachoron1.485633
...4Dshafipto+32tet (?)1.485633
shaha2Dsmall hexahexaapeirogonal tiling
shahoh4Dsmall hexadecahemihexadecachoron1
shanq7Dsmall demifiedhecatonicosihexapentacosiheptacontihexaexon2
shappy, 7/2-pyr3Dsmall heptagrammic pyramid0.650389
shasc4Dsmall heptagrammicscalene, small-heptagrammic-pyramidal pyramid, line atop fully orthogonal small heptagramm0.658240
sheat2Dstellated heptagonal tiling, hyperbolic order 7 heptagram tiling0.484510i
shexah3Dhyperbolic order 4hexagonal-tiling honeycomb0.707107i
shexat2Dhyperbolic order 4 hexagonal tiling0.707107i
shexatip3Dhyperbolic x x6o4o tesselation0.5i
shi4Dsnub hecatonicosachoron (butnotsnahi)2.739576
shiddip, K-4.544Dsquare - hexagon duoprism1.224745
shihi4Dsmall hecatonicosihecatonicosachoron5.854102
shihix4Dsmall hecatonicosihecatonicosihexacosachoron2.975584
shihtip6Dsquare-hexagon-hexagon triprism1.581139
shilq7Dsmall demified pentacontihexapentacosiheptacontihexaexon2.179449
shinhi4Dsmall hecatonicosintercepted hecatonicosachoron4.534568
ship3Dbistrophic heptagrammic prism, heptagrammic prism of winding number 2, small heptagrammic prism, small stellated heptagonal prism0.811783
shipady4Dsmall hecatonicosiprismatodishecatonicosachoron1.814331
shitte4Dhyperbolic order 4hecatonicosachoric tetracomb0.899454i
shopjak6Dsmall demiprismatedicosiheptaheptacontidipeton1.914854
shopjaka7Dshopjak alterprism,shopjak atop alternateshopjak,rojak-first medial segment ofbranq1.936492
shorjak6Dsmall demirhombatedicosiheptaheptacontidipeton3.265986
shothat, (inbetween: shath)2Dsmall hexagonal-trigonal-hexagonal tiling
si3Dsnub icosahedron,compound of 10oct (butnotgissi)0.707107
sibacadint5Dsmall biprismatocellidispenteractitriacontaditeron2.379961
sibcaxh6Dsmall bicellated hexeractic pentacomb
sibcotdin5Dsmall biprismatocellitriacontadiadispenteract3.534493
siborg6Dsmall birhombatedhexacontitetrapeton, bicantellated hexacross, rectifiedbirectified-hexacontitetrapeton2.236068
sibpo7Dsmall biprismated octaexon, biruncinated octaexon1.561250
sibpof6Dsmall biprismatedtetradecapeton, biruncinatedheptapeton1.414214
sibrant5Dsmall birhombatedpenteractitriacontiditeron, bicantellatedpenteract, bicantellatedpentacross2.236068
sibricot4Dsmall birhombated icositetrachoric tetracomb, grand prismatodisicositetrachoric tetracomb
sibrid (old: sadrid)5Dsmall birhombateddodecateron, bicantellatedhexateron, equatorial cross-section ofscad-firsttrim, equatorial cross-section ofrix-firstbrox1.414214
...5Disomorph ofsmall birhombated dodecateron0.816497
sibridacard6Dsibrid atopcard, first subsegment ofdot-firstram1.732051
sibtadin5Dsmall biprismatotriacontadiadispenteract3.047217
sicdatrid3Dsmall complex (ditrigonary) rhombicosidodecahedron0.866025
sichado4Dsmall cubihexadecadisoctachoron2.370932
sid pippadia5Dsid pippady alterprism2.527959
sid pippady4Dsmall dipentary prismatodishecatonicosachoron2.497212
sid thipady4Dsmall ditrigonary hecatonicosiprismatodishecatonicosachoron1.814331
sid tipathi4Dsmall ditrigonary prismatotriakishecatonicosachoron4.179968
sidacadint5Dsmall discellidispenteractitriacontaditeron2.379961
siddapady4Dsmall disprismatodishecatonicosachoron2
siddatady4Dsmall ditetrahedral dishecatonicosachoron2.288246
siddatchi4Dsmall ditetrahedronary cubihecatonicosachoron2.288246
siddic4Dsmall distetracontoctachoron1.847759
siddid (old: siided)3Dsnub dodecadodecahedron, chaugnar faugn
siddiddip4Dsnub-dodecadodecahedron prism
siddit paxhi4Dsmall ditetrahedronary hexacosidishecatonicosachoron2.288246
siddit thix4Dsmall ditrigonal trishecatonicosihexacosachoron1.732051
sidditdid3Dsmall ditrigonary dodekicosidodecahedron, small dodekified icosidodecahedron1.721489
sidditdiddip4Dsmall-ditrigonary-dodekicosidodecahedron prism1.792631
sidditdy4Dsmall ditrigonary dishecatonicosachoron1.732051
sidditpix4Dsmall ditrigonary prismatohexacosichoron1.732051
siddo3Dsnub disoctahedron, octahedralcompound of 2ike,vertex figure ofsody0.951057
siddy3Dsmall dodekicosahedron1.721489
...3Dsiddy+12{10/4} (?)1.721489
...3Dsiddy+20{6/2} (?)1.721489
siddykid3Dsmall didyakis dodecahedron
sided3Dsnub icosidodecadodecahedron, dagon1.126898
sidhei3Dsmall dodecahemicosahedron, great dodecahemiicosahedron (butnotgidhei)1
sidhid3Dsmall dodecahemidodecahedron1.618034
sidhiquit paddy4Dsmall dishecatonicosaquasitruncated prismatodishecatonicosachoron5.605034
sididdip4Dsnub-icosidodecadodecahedron prism
sidipthi4Dsmall dipental trishecatonicosachoron2.497212
siditetpeat2Dsmall ditetragonary tetrapentagonal tiling, hyperbolic x4o4o5/2*a tiling0.786151i
sidpicdoh3Dhyperbolic small disprismated cubical-dodecahedral honeycomb, hyperbolic prismated order 5 cubic honeycomb, hyperbolic runcinated order 5 cubic honeycomb, hyperbolic prismated order 4 dodecahedral honeycomb, hyperbolic runcinated order 4 dodecahedral honeycomb1.723155i
sidpichexah3Dhyperbolic small disprismatedcubic-hexagonal-tiling honeycomb, hyperbolic prismated order 6 cubical honeycomb, hyperbolic runcinated order 6 cubical honeycomb1.313295i
...5Dsid pippadia + 240 2sissid2.527959
...4Dsidpippady+120 2sissid (?)2.497212
sidpith4Dsmall disprismatotesseractihexadecachoron, runcinatedtesseract, small prismated tesseract1.485633
..., sidpith || prit5D(degenerate)sidpith atopprit∞   i.e. flat in euclidean space
..., sidpith || tat5D(degenerate)sidpith atoptat∞   i.e. flat in euclidean space
sidpithexah3Dhyperbolic small disprismatedtetrahedral-hexagonal-tiling honeycomb, hyperbolic prismated tetrahedral honeycomb, hyperbolic runcinated tetrahedral honeycomb, hyperbolic runcinated hexagonal tiling honeycomb1.931852i
sidpithip5Dsmall-disprismatotesseractihexadecachoron prism, runcinated-tesseract prism, small-prismated-tesseract prism, central segment ofscant1.567516
sidpixathi4Dsmall dipentagonal hexacositrihecatonicosachoron2.497212
sidpixhi4Dsmall disprismatohexacosihecatonicosachoron, runcinatedhecatonicosachoron, runcinatedhexacosachoron5.236068
..., sidpixhi || srix5D(degenerate)sidpixhi atopsrix∞   i.e. flat in euclidean space
sidpixhip5Dsmall-disprismatohexacosihecatonicosachoron prism, runcinated-hecatonicosachoron prism, runcinated-hexacosachoron prism5.259887
sidrebcu4Dstellidodecahedral rectibicupola,orbiform bistratc stack ofsmall stellated dodecahedron atop pseudododecadodecahedron atopgreat dodecahedron1.064815
sidsrahi4Dswirl-diminishedsmall rhombated hecatonicosachoron, swirl-diminished cantellated hecatonicosachoron6.735034
sidtaxady4Dsmall ditetrahedronary hexacosidishecatonicosachoron2.288246
sidtaxhi4Dsmall ditetrahedronary hexacosihecatonicosachoron2.288246
sidtaxhiap5Dsmall ditetrahedrary hexacontahecatonicosachoron antiprism2.321762
sidthidy hi4Dsmall ditrigonal hecatonicosadishecatonicosihecatonicosachoron1.732051
sidthixhi4Dsmall ditrigonary hecatonicosihexacosihecatonicosachoron1.773668
sidtid3Dsmall ditrigonary icosidodecahedron, holosnub dodecahedron,vertex figure ofsidtixhi0.866025
...3Dsidtid+ditdid (?)0.866025
...3Dsidtid+ditdid+gidtid (?)0.866025
...3Dsidtid+gidtid (?)0.866025
sidtidap4Dsmall-ditrigonary-icosidodecahedron antiprism0.951057
sidtidasiid4Dsmall ditrigonary icosidodecahedron atopsmall icosicosidodecahedron,sidtid cap ofstut phiddix3.835128
sidtiddip4Dsmall-ditrigonary-icosidodecahedron prism1
sidtidpy4Dsidtid pyramid, vertex pyramid ofsidtixhi1
sidtixhi4Dsmall ditrigonary hexacosihecatonicosachoron1
...4Dsidtixhi+dox (?)1
sidtixhipy, pt || sidtixhi5D(degenerate)sidtixhi pyramid∞   i.e. flat in euclidean space
sidtixhiu5Dsidtixhi-based ursateron1.008123
sifdahihox4Dsmall fissary dodecahedronary hecatonicosihemihexacosachoron1
sifodib3Dsidtidfaceting sidtid-0-10-20-2 (i.e. with 10(=d) {3}, 20(=i) {4}, and 2(=b) {5})0.866025
siid3Dsmall icosicosidodecahedron1.721489
siida (alt.: siidcup)4Dsmall icosicosidodecahedral alterprism,small icosicosidodecahedral cupoliprism, closersiid atopsiid1.765796
siidip4Dsmall-icosicosidodecahedron prism1.792631
sik vadixady4Dsmall skewverted dishexacosidishecatonicosachoron4.684471
sik vipathi4Dsmall skewverted prismatotriakishecatonicosachoron2.828427
sik vixathi4Dsmall skewverted hexacositriakishecatonicosachoro4.684471
sikvacadint5Dsmall skewverted cellidispenteractitriacontaditeron1.859330
..., s∞o2o3x6s3D...
..., s∞o2s3s6s3Dfull snub triangular prismatic honeycomb
..., s∞o2s3s6x3Dedge-snub triangular prismatic honeycomb
..., s∞o2s4s4s3Dfull snub square prismatic honeycomb
...3Dedge-snub square prismatic honeycomb
..., s∞o2s4x4s3Dedge-snub square prismatic honeycomb
..., s∞o2s4x4x3Dalternating bistratictosquat honeycomb
..., s∞o2x3x6s3Dalternating bistratichexat honeycomb
..., s∞o2x4s4x3Dsquare-snub square prismatic honeycomb
..., s∞x2o3x6s3D...
..., s∞x2s3s6s3Daxial edge-snub triangular prismatic honeycomb
sinnont5Dsmall penteractipenteractitriacontiditeron1.567516
sinnontip6Dsinnont prism1.645329
siphado4Dsmall prismatohexadecadisoctachoron2.613126
siphatit4Dsmall diprismatodemitesseractic tetracomb, steric tesseractic tetracomb
siphidy4Dsmall prismated hecatonicosadishecatonicosachoron4.917351
siphin5Dsmall prismatedhemipenteract, runcinated demipenteract, stericpenteract1.274755
siphina6Dsiphin alterprism, medial segment ofsochax1.322876
siphinnip6Dsmall-prismated-hemipenteractic prism1.369306
sipped3Dstellatedhyperbolic order 5 dodecahedral honeycomb0.475273
sipthi4Dsmall prismatotriakishecatonicosachoron1.878261
sipti4Dsmall prismatotriakisicositetrachoron3.498949
sirc4Dsmall retrotetracontoctachoron1.847759
sircaptint (old: srecaptint)5Dsmall retrocelliprismatotruncated penteractitriacontaditeron3.701317
sircarn5Dsmall retrocellirhombated penteract2.660531
sirco (alt.: esquobcu)3Dsmall rhombicuboctahedron, expandedoctahedron, expandedcube, elongatedsquare-orthobicupola1.398966
sirco acope5Dsmall-rhombicuboctahedron atopcuboctahedron-prism1.502958
sirco aticu4Dexpanded axially-octahedral ursachoron, (sirco,tic)-based ursulate1.806144
sircoa gircotum4Dbistratic cap ofprismatorhombated tesseract, rhombicuboctahedral rotunda, (sirco,girco)-based tutschoron, (sirco,girco)-based tutism2.370932
sircoa ticcup5Dsmall-rhombicuboctahedron atoptruncated-cube-prism2.207107
sircoagirco, sirco || girco4D(degenerate)small rhombicuboctahedron atopgreat rhombicuboctahedron∞   i.e. flat in euclidean space
sircoatic, sirco || tic, K-4.1004Dsmall rhombicuboctahedron atoptruncated cube,small-rhombicuboctahedral cap ofsmall rhombated tesseract1.847759
sircoatoe, sirco || toe, K-4.754Dsmall rhombicuboctahedron atoptruncated octahedron1.582890
sircope, K-4.664Dsmall-rhombicuboctahedron prism, medial (cube-first) subsegment ofsidpith1.485633
sircotic6Dsmall-rhombicuboctahedron - truncated-cube duoprism2.263033
sird3Dsmall rhombidodecahedron2.232951
...3Dsird+12{10/2}2.232951
...3Dsird+20{6/2} (?)2.232951
sirdatady4Dsmall retroditetrahedral dishecatonicosachoron2.288246
...4Dsirdatady+1440{5/2}2.288246
sirdo4Dsmall rhombic disoctachoron1.847759
sirdop4Dsmall rhombidispentachoron1.183216
...4Dsirdop+10{6/2} (?)1.183216
sirdtapady4Dsmall retroditetrahedronary prismatodishecatonicosachoron2.288246
...4Dsirdtapady+600 2tet (?)2.288246
sirdtaxadiap5Dsmall retroditetrahedronary hexacosidishecatonicosachoron atop alternatesmall retroditetrahedronary hexacosidishecatonicosachoron,small retroditetrahedronary hexacosidishecatonicosachoron alterprism2.321762
sirdtaxady4Dsmall retroditetrahedronary hexacosidishecatonicosachoron2.288246
sirfix4Dsmall rhombated faceted hexacosachoron4.352502
sirfixady4Dsmall retrofrustary hexacosidishecatonicosachoron2.236068
sirfixthi4Dsmall retrofrustic hexacositrishecatonicosachoron2.236068
sirfthi4Dsmall retrofrustary trishecatonicosachoron2.236068
...3Dvertex figure ofsmall retrofrustary trishecatonicosachoron0.816497
sirgaghi4Dsmall rhombated great grand hecatonicosachoron1.513868
sirgashi4Dsmall rhombated grand stellated hecatonicosachoron1.589926
sirgashia5Dsmall rhombated grand stellated hecatonicosachoron alterprism1.618034
sirgaship5Dsmall-rhombated-grand-stellated-hecatonicosachoron prism1.666693
sirgax4Dsmall rhombated grand hexacosachoron1.054256
sirghi4Dsmall rhombated great hecatonicosachoron3.387054
sirghia5Dsmall rhombated great hecatonicosachoron alterprism3.404434
sirghipe5Dsmall-rhombated-great-hecatonicosachoron prism3.423760
sirgikaike4Dsmall retrogikaike1
sirhax6Dsmall rhombatedhemihexeract, cantellated demihexeract, runcichexeract1.936492
sirhesa7Dsmall rhombatedhemihepteract, cantellated demihepteract, runcichepteract2.207940
sirhin5Dsmall rhombihemipenteract, cantellated demipenteract, runcicpenteract1.620185
...5Disomorph ofsmall rhombihemipenteract0.790569
sirhina6Dsirhin alterprism, medial segment ofsophax1.658312
sirhinasart6Dsirhin atopsart,nit-first subsegment ofram1.732051
sirhinathin6Dsmall rhombated hemipenteract atoptruncated hemipenteract,small rhombated hemipenteract-first cap ofsmall rhombated hemihexeract1.936492
sirjak6Dsmall rhombatedicosiheptaheptacontidipeton2.380476
sirlaq7Dsmall rhombated pentacontihexapentacosiheptacontihexaexon3.316625
sirn5Dsmall rhombatedpenteract, cantellated penteract2.207107
sirnoh5Dsmall rhombated penteractic honeycomb
sirpaxhi4Dsmall rhombiprismic hexacosahecatonicosachoron9.744610
sirpdi4Dsmall rhombiprismic disicosatetrachoron3.498949
sirpdo4Dsmall rhombiprismatodisoctachoron2.370932
sirphinady4Dsmall inverted retropental hecatonicosaintercepted dishecatonicosachoron3.077684
sirpin5Dsmall retroprismated penteract1.914214
sirpith4Dsmall rhombiprismated tesseractihexadecachoron2.613126
sirsashi4Dsmall rhombated small stellated hecatonicosachoron3.963358
sirsei3Dsmall retrosnub icosiicosahedron,compound of 5gike0.587785
sirsid3Dsmall (inverted) retrosnub icosicosidodecahedron, retrosnub disicosidodecahedron, yog sothoth0.580695
sirsiddip4Dsmall-(inverted)-retrosnub-icosicosidodecahedron prism0.766294
sirsido3Dsmall retrosnub disoctahedron,compound of 2gike0.587785
sis3Dsmall snubihedron,compound of 6tet (butnotsnu)0.612372
sisdipthi4Dsmall stellated dipental trishecatonicosachoron2.497212
...4Dsishi+gaghi+120did (?)1
...4Dsishi+gaghi+idhi (?)1
...4Dsishi+gridixhi (?)1
...4Dsishi+idhi (?)1
...4Dsishi+ofiddady (?)1
...4Dsishi+paphicki+gridaphi (?)1
sishi, spD4Dsmall stellatedhecatonicosachoron, stellated polydodecahedron1
..., sishi || fix5D(degenerate)sishi atopfix, (degenerate)sishi antiprism, (degenerate)fix antiprism∞   i.e. flat in euclidean space
sishia5Dsmall stellated hecatonicosachoron alterprism, narrowersishi atopsishi1.074481
...5Dsishia + 22sishi1.074481
sishipy, pt || sishi5D(degenerate)sishi pyramid∞   i.e. flat in euclidean space
sishitte4Dhyperbolic (order 3) small-stellated-hecatonicosachoral tetracomb0.242934i
sisp4Dsmall swirlprism1.618034
sisquah3Dhyperbolic order 4square-tiling honeycomb, hyperbolic honeycomb with seed point at vertex of right-angledoctahedron domain0i
sisro3Dstar stellarotunda, half ofgreat icosidodecahedron0.618034
sissid3Dsmall stellateddodecahedron, penta-stellahedron,vertex figure ofgofix0.587785
sissid || 3doe4D(degenerate)sissid atop3doe∞   i.e. flat in euclidean space
...3Dsissid+3gike (?)0.587785
sissidadid, sissid || did4Dsmall stellated dodecahedron atopdodecadodecahedron,small-stellated-dodecahedralcupola1.064815
sissidadoe4D(degenerate)sissid atopdoe∞   i.e. flat in euclidean space
sissidagad, sissid || gad4Dsmall stellated decahedron atopgreat dodecahedron,sissid antiprism,gad antiprism1
sissidaraded, sissid || raded4Dsmall stellated dodecahedron atoprhombidodecadodecahedron,sissid-first cap ofpadohi2.497212
sissiddip4Dsmall-stellated-dodecahedron prism0.771681
sissiddow7Dsissidic disphenoid,sissidic duopyramid,sissid atop fully orthogonalsissid0.831254
sissidisc5Dsmall-stellated-dodecahedralscalene,small-stellated-dodecahedral-pyramid pyramid, line atop fully orthogonalsmall stellated dodecahedron0.636010
sissidpy4Dsmall-stellated-dodecahedral pyramid, vertex cap of unitgofix, vertex cap of v-scaledgohi0.618034
sistadip4Dsquare-pentagram duoprism0.881132
sistadow5D(square,pentagram)-disphenoid, (square,pentagram)-duopyramid, square atop fully orthogonal pentagram0.707107
sistic4Dsmall stellated icositetrachoron,compound of 6hex,compound of 2stico0.707107
sistodip4Dsquare - octagram duoprism0.890446
sistople (old: stodop)4Dsquare-octagram plus-prism, octagram diorthoprism,compound of 2sistodip1.485633
sit thixady4Dsmall tritrigonal hecatonicosihexacosidishecatonicosachoron3.835128
sitphi4Dsmall tripesic hecatonicosachoron2.288246
sitpodadia5Dsmall (intersected) tripesic dodecahedronary dishecatonicosachoron alterprism1.074481
sitpodady4Dsmall (intersected) tripesic dodecahedronary dishecatonicosachoron1
sittiteteat2Dhyperbolic rectified ditetragonary tritetragonal tiling, hyperbolic small tritetratetragonal tiling, hyperbolic cantic order 4 hexagonal tiling1.060082i
sittitetrat2Dhyperbolic shieldotritetragonal tiling, hyperbolic ditrigonary tritetratrigonal tiling, hyperbolic cantic octagonal tiling1.446026i
sitwadip4Dsquare - dodecagon duoprism2.057195
six fipady4Dsmall hexacosafaceted prismatodishecatonicosachoron5.236068
sixathi4Dsmall hexacositriakishecatonicosachoron2.351141
...4Dsix fipady+1200tet (?)5.236068
sixhidy4Dsmall hexacosihecatonicosadishecatonicosachoron2.975584
sixhihy4Dsmall hexacosihecatonicosihecatonicosachoron5.236068
sixipady4Dsmall hexacosiprismatodishecatonicosachoron6.881910
skatbacadint5Dsmall skewtrigonary biprismatocellidispenteractitriacontiditeron1.5
skevatant5Dsmall skewverted trispenteractitriacontaditeron1.859330
skiv datapixady4Dsmall skewverted ditrigonary prismatohexacosadishecatonicosachoron4.684471
skiv datixathi4Dsmall skewverted ditrigonary hexacosatrishecatonicosachoron4.684471
skivbadant5Dsmall skewverted biprismatodispenteractitriacontaditeron1.859330
skivcadach3Dsmall skewverted cubatiapeiroducubatic honeycomb
skiviphado4Dsmall skewverted prismatohexadecadisoctachoron1.414214
skivpacoca3Dsmall skewverted prismatocubaticubatiapeiratic honeycomb
skovactaden5Dsmall skewverted cellitriacontadiadispenteract1.859330
sladid (old: sit)3Dsmall lanceal disdodecahedron, strombic icositetrahedron, deltoidal icositetrahedron, tetragonal icosikaitetrahedron
sladit3Dsmall lanceal ditriacontahedron, strombic hexecontahedron, deltoidal hexecontahedron, tetragonal hexecontahedron
snadow, J843Dsnub disphenoid, snub digonal antiprism
snan5Dsnub penteract, alternation ofgreat cellated penteractitriacontiditeron...
snappoth4Dsmall spinoprismatotesseractihexadecachoron1.485633
snasquat2Dsnub square tiling
snatazt2Dhyperbolic snub trigonal-horocyclic tiling, hyperbolic snub triapeirogonal tiling, snub triapeirogonal tiling
snathaph3Dsnub trigonal-hexagonal prismatic honeycomb
snathat2Dsnub trihexagonal tiling
snathet2Dhyperbolic snub triheptagonal tiling
snatoct2Dhyperbolic snub trioctagonal tiling
sne3Dsnub icosiicosahedron,compound of 5ike0.951057
snet4Ds3s3s4s, snub tesseract, non-uniform alternation ofgidpith...
sni (old: snico) / snoc4Ds3s4s3s, (fully) snubbed icositetrachoron (butnotsadi) / snubbed tetracontoctachoron, non-uniform alternation ofgippic...
snic3Dsnubcube, snubcuboctahedron1.343713
sniccap4Ds2s3s4s, snub-cubic antiprism, non-uniform alternation ofgircope...
sniccup, K-4.604Dsnub-cube prism, snub-cuboctahedron prism1.433724
snich, s4s3s4s3D(full) snub cubical honeycomb, snub bicubic honeycomb
snid3Dsnubdodecahedron, snubicosidodecahedron2.155837
sniddap4Ds2s3s5s, snub-dodecahedral antiprism, non-uniform alternation ofgriddip...
sniddip, K-4.1104Dsnub-dodecahedron prism, snub-icosidodecahedron prism2.213060
snifthi4Dsmall spinofrustary trishecatonicosachoron2.236068
...3Dvertex figure ofsmall spinofrustary trishecatonicosachoron0.816497
snip / snad4Ds3s3s3s, snub pentachoron / snub decachoron, non-uniform alternation ofgippid...
snippit (old: spitac, alt.: snahin)5Dsnub prismatotriacontaditeron, snubdemipenteract, alternation ofgreat prismated triacontaditeron...
snisquap, J853Dsnub square antiprism
snit3Dpyritohedron, pyritosnub tetrahedron,o2o2o symmetricike variant,vertex figure ofhyperbolic cube + n-prism honeycombsqrt[a2+c2]
snit3Dpyritohedron, pyritosnub tetrahedron, vertex alternatedtoe1.581139
snixhi (old: snahi)4Ds3s3s5s, snub hexacosihecatonicosachoron, (snub hecatonicosachoron (butnotshi)), non-uniform alternation ofgidpixhi...
sno3Dsnub octahedron,compound of 4oct0.707107
snod (snix)5Dsnub dodecateron (snub hexateron), alternation ofgreat cellated hexateron...
snu3Dsnubihedron,compound of 6tet (butnotsis)0.612372
...3Dcomplex polyhedronsp-4-o2-3-o2, (γp3)/psqrt(3/8) / sin(π/p)
...4Dcomplex polychoronsp-4-o2-3-o2-3-o2, (γp4)/p
so3Dstella octangula, star tetrahedron,compound of 2tet0.612372
sobath3Dsmall biambotetrahedral honeycomb
sobcated4Dsmall bicuntitruncateddecachoron, general variant of expanded decachoron, general variant of expandedbidecasqrt[(2a2+3ab+3b2+2ac+4bc+3c2)/5]
sobcotic4Dsmall bicuntitruncatedtetracontoctachoron, general variant of expanded tetracontoctachoron, general variant of expandedbicontsqrt[a2+3ab+3b2+2ac sqrt(2)+4bc sqrt(2)+3c2]
sobpoxog6Dsmall biprismatedhexeractihexacontatetrapeton, biruncinated hexeract, biruncinated hexacross2.345208
sobteb8Dsmall biteratedbi-enneazetton, bipentellatedenneazetton1.414214
socat2Dhyperbolic order 4 octagon tiling0.594604i
socco3Dsmall cubicuboctahedron1.398966
soccope4Dsmall-cubicuboctahedron prism1.485633
soccopen7D(socco,pen)-duoprism1.535287
socdip4Dstellated-octagonal duoprism,compound of 4tes inodip army1
sochax6Dsmall cellatedhemihexeract, stericated demihexeract, pentichexaract, equatorial cross-section ofhax-firstlin1.322876
sodip, K-4.704Dsquare - octagon duoprism1.485633
sody4Dsmall deckishecatonicosachoron, snub decahecatonicosachoron,compound of 10ex inhi army,compound of 2spohi1.618034
sook8Dsmall octeractiocteractidiacosipentacontahexazetton1.790840
sophax6Dsmall prismatedhemihexeract, runcinated demihexeract, sterichexeract1.658312
sophi4Dsmall prismatohecatonicosachoron3.077684
sophip5Dsmall-prismatohecatonicosachoron prism3.118034
sople (old: odop)4Dsquare-octagon plus-prism, octagonal diorthoprism,compound of 2sodip1.485633
sorcpit5Dsmall retrocelliprismated triacontiditeron2.878460
soro8Dsmall rhombated octeract, cantellated octeract3.040171
sososaz7Dsmall hepteractihepteractihecatonicosoctaexon1.719624
sossa2Dsmall squarisquariapeirogonal tiling
sost2Dsquarisquaritiling
sotho8Dsmall terated hemiocteract, hexic octeract1.732051
soxaxog6Dsmall hexeractihexeractihexacontitetrapeton1.645329
soxaxogip7Dsoxaxog prism1.719624
soxeb8Dsmall exiated bi-enneazetton, heptellated enneazetton, expanded enneazetton,lattice A8 contact polytope (span of its roots), equatorial cross-section ofrene-firstriv1
spacyxh5Dsmall prismated cyclohexateric honeycomb
spaht4Dsmall prismated hexadecachoric tetracomb, small disicositetrachoric tetracomb, runcinated demitesseractic tetracomb
spam (old: skopam)6Dsmall prismatedpentacontitetrapeton, (small hebdomecontadiaprismated pentacontitetrapeton)2.236068
span5Dsmall prismatedpenteract, runcinated penteract1.914214
spapivady4Dsmall pentagrammal antiprismatoverted dishecatonicosachoron1.175571
spaquinoh5Dsmall prismated quarterpenteractic pentacomb, quarterpenteractic pentacomb
spat5Dsmall prismatedtriacontiditeron, runcinated pentacross1.870829
spaz7Dsmall prismated hecatonicosoctaexon, runcinated heptacross1.870829
spd{3,5,3}   (old: spt{3,5,3})3Dsemi partial diminishing (old: truncation) of hyperbolicorder 3 icosahedral tesselation0.509376i
spene8Dsmall prismated enneazetton, runcinated enneazetton1.452966
spepat2Dhyperbolic snub pentapentagonal tiling
...4Dhexaconta-sphenatedid-first deep parabidiminishedrahi...
sphiddix4Dsmall prismatohecatonicosadishexacosachoron6.881910
sphiddixa5Dsmall prismatohecatonicosadishexacosachoron alterprism6.893126
sphihix4Dsmall prismatohecatonicosahecatonicosahexacosachoron5.515107
sphixhi4Dsmall prismatohecatonicosihexacosihecatonicosachoron4.179968
spic4Dsmall prismatotetracontoctachoron, runcinatedicositetrachoron, expanded icositetrachoron1.847759
..., spic || srico5D(degenerate)spic atopsrico∞   i.e. flat in euclidean space
spiccup5Dsmall-prismatotetracontoctachoron prism, runcinated-icositetrachoron prism1.914214
spict4Dsmall prismated icositetrachoric tetracomb, small prismatotetracontaoctachoric tetracomb, runcinated icositetrachoric tetracomb
spid4Dsmall prismatodecachoron, runcinatedpentachoron, expanded pentachoron, pyroperichoron,tetaco gyrobicupola,vertex figure ofcypit,lattice A4 contact polytope (span of its roots), equatorial cross-section ofpen-firstscad, equatorial cross-section ofrap-firstrat1
spida rappip6Dspid ||rappip, (rap,rap,spid)-trigonic1
spidadeca, spid || deca5D(degenerate)spid atopdeca∞   i.e. flat in euclidean space
spidapenp6Dspid atoppenp, wedge ofstaf1
spidaprip5Dspid atopprip,spid-first monostratic cap ofspat1.870829
spidasrip5Dspid atopsrip,spid-first cap ofspix1.190238
spidasripu5D(spid,srip)-based ursateron1.331369
spidatip5Dsmall-prismate-pentachoron atop alternatetruncated-pentachoron1.274755
spidded3Dhyperbolic small prismated disdodecahedral honeycomb, hyperbolic prismated order 5 dodecahedral honeycomb, hyperbolic runcinated order 5 dodecahedral honeycomb1.272020i
spiddih3Dhyperbolic (small) prismated order 3 icosahedral honeycomb, hyperbolic runcinated order 3 icosahedral honeycomb1.272020i
spiddihexah3Dhyperbolic small prismatodishexagonal-tiling honeycomb, runcinated order 6hexagonal-tiling honeycomb1i
spiddip5Dsmall-prismatodecachoron prism1.118034
spiddish3Dhyperbolic small prismated dissquare-tiling honeycomb0.840896i
spidditrah3Dhyperbolic small prismated distriangular-tiling honeycomb0.759836i
spidpy5D(degenerate)spid pyramid∞   i.e. flat in euclidean space
spidrico4Dswirlprismatodiminishedrectified icositetrachoron, 24-diminishedrectified icositetrachoron1.732051
spidrox (alt.: hidrox)4Dswirlprismatodiminishedrectified hexacosachoron, 120-diminishedrectified hexacosachoron3.077684
spidy4Dswirlprismattic dishecatonicosachoron,compound of 24starpedip1
spiffy8Dsmall petateddischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton2.236068
spil6Dsmall prismatedheptapeton, runcinated heptapeton1.309307
...5Dvertex figure ofspil0.924211
spila (old: spilal spil)7Dsmall prismated heptapeton atop invertedsmall prismated heptapeton1.322876
spittit (old: sidpitit)4Dsmall prismatotesseractic tetracomb, small diprismatotesseractic tetracomb, runcinated tesseractic tetracomb
spix5Dsmall prismatedhexateron, runcinated hexateron1.190238
...4Dq-laced {3} || gyrotrip,vertex figure ofsrix0.907485
spixa (old: spixalspix)6Dsmall prismated hexateron alterprism,small prismated hexateron atop invertedsmall prismated hexateron, medial segment ofdot-firstbirectified hexacontitetrapeton1.224745
spixady4Dsmall prismatohexacosadishecatonicosachoron8.278950
spixalsarx6Dspix atop invertedsarx1.290994
spixhihy4Dsmall prismatohexacosihecatonicosihecatonicosachoron9.744610
spixip6Dsmall-prismated-hexateron prism1.290994
spo7Dsmall prismated octaexon, runcinated octaexon1.391941
spog6Dsmall prismatohexacontitetrapeton, runcinated hexacross1.870829
spohi4Dsmall pentishecatonicosachoron, snub pentahecatonicosachoron, chiralcompound of 5ex inhi army1.618034
spojak6Dsmall prismatedicosiheptapeton2.768875
sporraggix4Dswirlprismatoreplenishedrectified grand hexacosachoron0.726543
spox6Dsmall prismatedhexeract, runcinated hexeract2.263033
sprapivady4Dsmall pentagonal retroprismatoverted dishecatonicosachoron3.077684
spriphi4Dsmall pseudorhombated prismatohecatonicosachoron6.735034
...4Dspriphi+600 2thah (?)6.735034
spript4Dsmall pseudorhombated prismatotesseract1.847759
...4Dspript+16 2thah (?)1.847759
spuho8Dsmall petated hemiocteract1.414214
spysp4Dsmall pyramidic swirlprism1.618034
squaco5Dsquare-cuboctahedron duoprism1.224745
squacu, J43Dsquare cupola1.398966
squacufbil4Dsquare-cupofastegia biluna,rotunda ofquawros, square atopsquobcu
squacupe, K-4.694Dsquare-cupola prism,cube atopoctagonal prism1.485633
squadedip, K-4.974Dsquare - decagon duoprism1.765796
squadinit5Dsquare-diminishednit1.224745
squadoe5Dsquare-dodecahedron duoprism1.569562
squaf, K-4.144Dsquare antifastegium, square -squap wedge, {4} || gyrocube, bidiminishedoctahedral antiprism0.879465
squagippid6Dsquare - great-prismated-pentachoron duoprism2.345208
squagirco5Dsquare great-rhombicuboctahedron duoprism2.423081
squagrid5Dsquare - great-rhombicosidodecahedron duoprism3.867584
squah3Dhyperbolic order 3square-tiling honeycomb, hyperbolic honeycomb with seed point in center of right-angledoctahedron domain0.707107i
squahex6Dsquare-hexadecachoron duoprism,vertex figure ofbraxh1
squahi6Dsquare-hecatonicosachoron duoprism3.769377
squahix7Dsquare -hexateron duoprism,hixip prism,vertex figure ofbro0.957427
squahop8Dsquare - heptapenton duoprism,vertex figure ofbarn0.963624
squap3Dsquare antiprism0.822664
...4Dcubiswirlic heptacontidichoron, twelvefold dissectedcubic polytwister, twelvefold dissected cubiter1.538189
...5Dsquap - square duoprism, {4}-wedge oftessap1.050501
squapen6Dsquare-pentachoron duoprism,vertex figure ofbersa0.948683
...4Dexternal blend of thesquare-antiprism prism and 2cube-pyramids,cubic-pyramid-biaugmentedsquare-antiprism prism
...4Dexternal blend of thesquare-antiprism prism and 2squap-pyramids,squap-pyramid-biaugmentedsquare-antiprism prism
squappip, K-4.194Dsquare-antiprism prism0.962692
squappy4Dsquare-antiprismatical pyramid0.879465
squapt4D(line-)square-antiprismatic tegum,square-antiprismatic bipyramid,square-pyramidal antiprism
squarahi6Dsquare - rectified-hecatonicosachoron duoprism4.589369
squarap6Dsquare - rectified-pentachoron duoprism1.048809
squarat7Dsquarerectified-triacontiditeron duoprism1.224745
squarico6Dsquare - rectified-icositetrachoron duoprism1.870829
squarit6Dsquare - rectified-tesseract duoprism1.414214
squarox6Dsquare - rectified-hexacosachoron duoprism3.157869
squasc (old: squippypy, alt: edihex), 4pyr-pyr, K-4.44Dsquare-scalene, square-pyramidal pyramid, line atop fully orthogonal square, 1/4-luna ofhex, 4tet rosette, edge-diminishedhex0.707107
squascop5Dsquasc prism, square-scalene prism, square atopcube0.866025
...4Dsquashed hexaconta-sphenatedid-first deep parabidiminishedrahi...
squasirco5Dsquare - small-rhombicuboctahedron duoprism1.567516
squasnic5Dsquare -snub-cube duoprism1.518409
squasnid5Dsquare -snub-dodecahedron duoprism2.268840
squasquasc5D{4} atopsquasc0.790569
squasquippy5Dsquare-squippy duoprism,squippyp prism1
squasrid5Dsquare - small-rhombicosidodecahedron duoprism2.342236
squat2Dsquare tiling, 2Dhypercubical honeycomb (δ2),Voronoi complex of squarelattice,Delone complex of squarelattice
squatap3Dsquare tiling antiprism
squatet5Dsquare-tetrahedron duoprism, square duofastegium, 2,4-duoprism cupoliprism,vertex figure ofbrox0.935414
squati5Dsquare - truncated-icosahedron duoprism2.576932
squatic5Dsquare - truncated-cube duoprism1.914214
squatid5Dsquare - truncated-dodecahedron duoprism3.052479
squatoe (old: squato)5Dsquare - truncated-octahedron duoprism1.732051
squatricu5Dsquare-tricu duoprism1.224745
squattip3Dsquare tiling prism
squatut5Dsquare - truncated-tetrahedron duoprism1.369306
squaw, K-4.64, {8} || squap4Dantitetrawedge, octagon -square-antiprismatic wedge, square gyrobicupolaic ring, {8} ||squap, {4} || gyratedsquacu1.447009
squazat2Dorder 4 apeirogonal tiling, hyperbolic order 4 horocyclic tiling0.5i
squepe6Dsquarepennene0.707107
squete5Dsquare-pyramidal pyramid pyramid, square-tettene, triangular-square disphenoid, triangular-square duopyramid, half of thetriacontiditeron0.707107
squex6Dsquare-hexacosachoron duoprism1.765796
squico6Dsquare-icositetrachoron duoprism1.224745
squicuf, K-4.734Dsquare cupofastegium, octagon -cube wedge ofsidpith, square orthobicupolaic ring, {8} ||cube, {4} ||squacu, 1/4-luna ofquawros1.485634
squicuffip5Dsquicuf prism,tes atopop1.567516
squid5Dsquare-icosidodecahedron duoprism1.765796
squiddaf5Dsquare duoantifastegium, digonal-square duoantiwedge,square prism atop bidualsquare prism0.895420
squigybcu, J293Dsquare gyrobicupola
squike5Dsquare-icosahedron duoprism1.185120
squipdip, K-4.424Dsquare-pentagon duoprism1.106168
squippia squacu, K-4.1094Dsquare pyramid atopsquare cupola1.847759
squippiaco, K-4.314Dsquare-pyramid atopcuboctahedron1
squippiatricu, K-4.324Dsquare-pyramid atoptriangular-cupola1
squippy, 4pyr, J13Dtetragonal pyramid, half ofoct0.707107
squippyal cube (alt.: doctacube), K-4.164Dsquippy atop gyro cube, diminished octahedron atop cube0.879465
squippyippy5Dsquare-pyramidal-prismatic pyramid, half of vertex pyramid ofrectified triacontiditeron1
squippyp, K-4.124Dsquare-pyramidal prism, J1 prism, line ||cube, digonal magnabicupolaic ring0.866025
squipuf, K-4.1054Dsquare pucofastegium, square -octagon-prismatic wedge, square magnabicupolaic ring, {4} ||op, {8} ||squacu, square-cap ofsrit1.847759
squit3D(line) square tegum,Waterman polyhedron number 2 wrt. body-centered cubiclattice C3* centered at a hole
squix7Dsquarehixene, square atop fully orthogonalpentachoron0.707107
squobcu, J283Dsquare orthobicupola
squobcupe4Dsquare orthobicupola prism, J28 prism...
squoc9Dsquare - octaexon duoprism,vertex figure ofbrade0.968246
squoct5Dsquare-octahedron duoprism,vertex figure ofbrinoh1
sradditdahix4Dsmall retroditetrahedronary dishecatonicosihexacosachoron2.288246
sraghi4Dsmall rhombated grand hecatonicosachoron2.689994
srahi4Dsmall rhombatedhecatonicosachoron, cantellated hecatonicosachoron6.735034
..., srahi || xhi5D(degenerate)srahi atopxhi∞   i.e. flat in euclidean space
srahip (old: srahipe)5Dsmall-rhombated-hecatonicosachoron prism6.753568
sraht2Dsmall rhombihexagonal tiling
sram (old: skobram, skabram)6Dsmall rhombatedpentacontitetrapeton, (small hebdomecontadiabirhombated pentacontitetrapeton)3.316625
sranq7Dsmall rhombated hecatonicosihexapentacosiheptacontihexaexon2.645751
sratoh (old: ratoh)3Dsmall rhombated tetrahedral-octahedral honeycomb, runcinated alternated cubic honeycomb, runcinated tetrahedral-octahedral honeycomb, runcic cubic honeycomb
srawv ditathi4Dsmall retrosphenoverted ditrigonary triakishecatonicosachoron3.294556
srawv hidy4Dsmall retrosphenoverted hecatonicosadishecatonicosachoron3.387054
srawv hixhi4Dsmall retrosphenoverted hecatonicosihexacosihecatonicosachoron6.073594
srawvathi4Dsmall retrosphenoverted triakishecatonicosachoron4.352502
srawvixady4Dsmall retrosphenoverted hexacosadishecatonicosachoron6.735034
srek8Dsmall rhombated diacosipentacontahexazetton, cantellated octacross1.732051
srene8Dsmall rhombated enneazetton, cantellated enneazetton1.452966
srich3Dsmall rhombated cubic honeycomb, cantellated cubic honeycomb
srico4Dsmall rhombatedicositetrachoron, cantellated icositetrachoron2.613126
..., srico || cont5D(degenerate)srico atopcont∞   i.e. flat in euclidean space
..., srico || prico5D(degenerate)srico atopprico∞   i.e. flat in euclidean space
sricoa (old: sricoalsrico), srico || gyro srico5Dsmall-rhombated-icositetrachoron alterprism,small-rhombated-icositetrachoron atop gyratedsmall-rhombated-icositetrachoron2.632865
sricope (old: sripe)5Dsmall-rhombated-icositetrachoron prism, cantellated-icositetrachoron prism2.660531
sricot4Dsmall rhombated demitesseractic tetracomb, small prismatodisicositetrachoric tetracomb
srid3Dsmall rhombicosidodecahedron, expandedicosahedron, expandeddodecahedron2.232951
..., xFoFx3ooooo5xofox&#xt   (F=ff=x+f)4Dbilunabirotundic rhombicosidodecahedron prism, castellated rhombicosidodecahedral prism
srida gridtum4Dbistraticsrid-cap ofprahi, (srid,grid)-based tutsachoron, (srid,grid)-based tutism8.278950
sridaphi4Dsmall retroinverted dodecahedronary prismatohecatonicosachoron1
sridati, srid || ti, K-4.1264Dsmall-rhombicosidodecahedron atoptruncated-icosahedron2.485450
sridatid, K-4.1594Dsmall rhombicosidodecahedron atoptruncated dodecahedron,small-rhombicosidodecahedral cap ofsmall rhombated hecatonicosachoron6.735034
sridatidu4Dexpanded axially-icosahedral ursachoron, (srid,tid)-based ursulate3.077684
sriddip, K-4.1114Dsmall-rhombicosidodecahedron prism2.288246
sriddoh3Dhyperbolic (small) rhombated (order 4) dodecahedral honeycomb, hyperbolic cantelated order 4 dodecahedral honeycomb2.131920i
sridixhi4Dsmall retroinverted dodecahedronary hexacosahecatonicosachoron1
sridtathi4Dsmall retroinverted ditetrahedronary trishecatonicosachoron2.288246
srih3Dhyperbolic (small) rhombated order 3 icosahedral honeycomb, hyperbolic cantelated order 3 icosahedral honeycomb2.120267i
sril6Dsmall rhombatedheptapeton, cantellated heptapeton1.362770
srillip7Dsmall-rhombated-heptapeton prism1.451600
srip4Dsmall rhombatedpentachoron, cantellated pentachoron1.183216
sripa (alt: pabdinit, old: sripalsrip)5Dsmall rhombated pentachoron alterprism,small rhombated pentachoron atop invertedsmall rhombated pentachoron, parabidiminishednit, equatorial segment ofnit1.224745
sripa gippidtum5Dsrip-first bistratic cap ofpithin, (srip,gippid)-based tutsateron, (srip,gippid)-based tutism2.371708
sripadeca5Dsrip atopdeca,srip-first half ofsibrid1.414214
sripadecu5D(srip,deca)-based ursateron1.514954
sripady4Dsmall rhombiprismic dishecatonicosachoron8.278950
sripaf6Dsmall rhombated pentachoron antifastegium,small rhombated pentachoron atop invertedsmall-rhombated-pentachoral-prism1.290994
sripagrip5Dsrip atopgrip,srip-first cap ofsibrant2.236068
sripal pripu5D(srip,inv.prip)-based ursateron1.637956
sripalgrip, srip || inv grip5D(degenerate)srip atop invertedgrip∞   i.e. flat in euclidean space
sripalprip5Dsrip atop invertedprip,srip-first cap ofsart1.732051
sripaltip5Dsrip atop invertedtip1.274755
sripaprip5Dsrip atopprip,srip-first cap ofcard1.658312
sripatip5Dsrip atoptip,srip-first segment ofsarx1.290994
sripech3Dhyperbolic rhombated order 5 cubic tesselation, hyperbolic cantellated order 5 cubic tesselation2.053119i
sriphi4Dsmall retropental hecatonicosachoron3.077684
sripped3Dhyperbolic (small) rhombated order 5 dodecahedral honeycomb, hyperbolic cantelated order 5 dodecahedral honeycomb1.546658i
srippip5Dsmall-rhombated-pentachoron prism1.284523
srit4Dsmall rhombatedtesseract, cantellated tesseract1.847759
..., srit || proh5D(degenerate)srit atopproh∞   i.e. flat in euclidean space
sritaprohu5D(srit,proh)-based ursateron2.706827
sritrah3Dhyperbolic (small) rhombatedtriangular-tiling honeycomb1.467890i
srittip5Dsmall-rhombated-tesseract prism1.914214
srittit4Dsmall rhombitesseractic tetracomb, cantellated tesseractic tetracomb
srix4Dsmall rhombatedhexacosachoron, cantellated hexacosachoron6.073594
srixasrahi5D(degenerate)srix atopsrahi∞   i.e. flat in euclidean space
srixip5Dsmall-rhombated-hexacosachoron prism, cantellated-hexacosachoron prism6.094140
srocgrin5Dsmall retrocelligreat rhombated penteract3.988340
srocth3Dhyperbolic small rhombatedorder 4 octahedral honeycomb1.707107i
srog6Dsmall rhombihexacontitetrapeton, cantellated hexacross1.732051
sroh3Dsmall rhombihexahedron1.398966
...3Dsroh+8{6/2} (?)1.398966
srohp4Dsmall-rhombihexahedron prism1.485633
sroptin5Dsmall retroprismatotruncated penteract3.239235
srotazt2Dhyperbolic (small) rhombi-trigonal-horocyclic tiling1.322876i
srotehat2Dhyperbolic (small) rhombisquarehexagonal tiling1.405256i
sroteoct2Dhyperbolic (small) rhombitetraoctagonal tiling1.175154i
srotepet2Dhyperbolic rhombisquarepentagonal tiling1.794231i
srotezt2Dhyperbolic (small) rhombitetraapeirogonal tiling, hyperbolic rhombisquareapeirogonal tiling0.978318i
srothaph (old: rothaph)3D(small) rhombitriangular-hexagonal prismatic honeycomb
srothat (old: rothat)2D(small) rhombitrihexagonal tiling
srothet (old: sirthet)2Dsmall rhombitriheptagonal tiling, hyperbolic rhombitriheptagonal tiling2.728895i
srotoct (old: sirtoct)2Dhyperbolic (small) rhombitrioctagonal tiling2.096343i
srox6Dsmall rhombatedhexeract, cantellated hexeract2.515637
stacu3Dpentagrammic cupola, star cupola0.866025
stacupe4Dpentagrammic-cupola prism,stip atop2pip0.874032
stade5Dstellateddodecateron,compound of 2hix0.645497
stadidip4Ddecagram-decagram duoprism0.874032
stadow5Dpentagrammic disphenoid, pentagrammic duopyramid, pentagram atop fully orthogonal pentagram0.623054
staf (interim: stef)6Dsmall teratedtetradecapeton, pentellatedheptapeton, expanded heptapeton,lattice A6 contact polytope (span of its roots), equatorial cross-section ofhop-firstsuph, equatorial cross-section ofril-firstrez, equatorial cross-section ofhop-firstlaq1
stafe4Dstellar (pentagrammal) antifastegium, pentagram -stap wedge, {5/2} || gyrostip0.535857
stafip7Dsmall terated tetradecapeton prism1.118034
stai3Dsmall triambic icosahedron, first stellation of theicosahedron
stanq7Dsmall teratedhecatonicosihexapentacosiheptacontihexaexon1.658312
stap3Dbistrophic pentagrammic antiprism, stellar antiprism, 5/2-antiprism0.656431
stapedit4D({5/2},{5})-duotegum,tegum product of a pentagon and a pentagram
stapepy4Dpentagram-antiprismatical pyramid0.662791
stapper3Dstar pentagonal retrohedron0.866025
stappip4Dpentagramic-antiprism prism0.825168
stappy, 5/2-pyr3Dpentagrammic pyramid, stellated pentagonal pyramid0.587785
stappyp4Dpentagram-pyramidal prism, line ||stip0.771681
stardedip4Dpentagram - decagon duoprism1.701302
stardip4Dpentagram-pentagram duoprism0.743496
starodip4Dpentagram - octagon duoprism1.408368
starp (old: restap)3Dtristrophic pentagrammic antiprism, stellar retroprism (retrograde stellar antiprism), 5/3-antiprism0.587785
starpedip (old: stipdip, starpendip)4Dpentagram-pentagon duoprism, stellar (pentagonal) pentagonal diprism1
starpedippy, pt || starpedip5D(degenerate)starpedip pyramid∞   i.e. flat in euclidean space
starpglass3Dpentagrammic retroprismatic hourglass0.707107
starpglassdit6Dpentagrammic-retroprismatic-hourglass duotegum0.707107
starpglassit4Dpentagrammic-retroprismatic-hourglass tegum,pentagrammic-retroprismatic-hourglass bipyramid0.707107
stasc (old: stappypy)4Dstellarscalene, pentagrammicscalene, pentagram-pyramidal pyramid, line atop fully orthogonal pentagram, 5tet two-step rosette0.618034
stasissiddow6D(pentagramm,sissid)-disphenoid, (pentagramm,sissid)-duopyramid, pentagram atop fully orthogonalsmall stellated doedcahedron0.639240
stastidedip4Dpentagram - decagram duoprism0.811393
stastodip4Dpentagram - octagram duoprism0.754511
state5Dstellartettene, pentagrammictettene, pentagram-pyramidal pyramid pyramid, triangle atop fully orthogonal pentagram0.636010
staw4Dpentagrammic gyrobicupolaic ring, star antiwedge, {10/2} ||stap0.870153
stawros4Dpentagrammic ({10} || pip-)wedge rosette, bridge cyclopentaaugmentedstarpedip, ring-augmentedstarpedip
sted4Dstellateddecachoron,compound of 2pen0.632456
stef6Dstellatedtetradecapeton,compound of 2hop0.654654
stefacoth4Dsmall tesseractifaceted cubitesseractihexadecachoron1.485633
stepet2Dhyperbolic snub tetrapentagonal tiling
steth4Dsmall tesseractitesseractihexadecachoron1.485633
stethip5Dsmall-tesseractitesseractihexadecachoron prism1.567516
stico (old: sico)4Dstellated icositetrachoron, stella tegmata,compound of 3hex0.707107
stiddip3D(tristrophic) decagrammic prism, stellated decagonal prism, 10/3-prism, 10-prism with winding number 30.794963
stidox4Dstellated dodecahedral hexacosachoron,compound of 75hex inex army,compound of 25stico inex army0.707107
stip3Dstellated pentagonal prism, 5/2-prism, 5-prism with winding number 2,vertex figure ofraggix0.725530
stippy4Dstellated-pentagonal prismatic pyramid, vertex pyramid of therectified grand hexacosachoron0.726543
stiroh7Dsmall trirhombihexadecaexon, tricantellatedoctaexon1.732051
stisaw4Dreduced pentagrammic gyrobicupolaic ring, star semiantiwedge, pseudo {10/2} ||stap0.870153
stiscu3Dpentagrammic cuploid, star semicupola0.866025
stititet2Dhyperbolic snub tritritetragonal tiling, hyperbolic snub tiling of family o3o3o4*a
sto4Dsmall trisoctachoron, small triakisoctachoron1.224745
...4Dsto+16tet (?)1.224745
stoap, 8/3-ap3Doctagrammic antiprism0.672673
stoc4Dstellated tetracontoctachoron,compound of 2ico1
stoct5Dpentagram - octahedron duoprism0.881132
stodatixhi4Dsmall toroidoditrigonary hexacosihecatonicosachoron1.732051
stodip4Doctagram-octagram duoprism0.765367
stoditpix4Dsmall toroidoditrigonary prismatohexacosichoron1.732051
stohix7Doctagram -hexateron duoprism0.842354
stop (old: sop)3D(tristrophic) octagrammic prism, stellated octagonal prism, 8/3-prism, 8-prism with winding number 30.736813
stopen6Doctagram-pentachoron duoprism1.092197
stopper3Dstar pentagonal rhombihedron0.866025
stotet5Doctagram-tetrahedron duoprism, octagram duofastegium0.817247
stotoe5Doctagram truncated-octahedron duoprism, star-octagon truncated-octahedron duoprism1.671195
stotut5Doctagram - truncated-tetrahedron duoprism1.291469
stowoct5Doctagram octahedron duoprism0.890446
stoxog6Dsmall teratedhexeractihexacontatetrapeton, pentellatedhexeract, pentellatedhexacross1.645329
stut cadoca3Dsmall tritrigonary cubatidicubatiapeiratic honeycomb
stut dixady4Dsmall tritrigonal dihexacosidihecatonicosachoron3.835128
stut phiddix4Dsmall tritrigonal prismatohecatonicosidishexacosachoron3.835128
stut phiddixa5Dsmall tritrigonal prismatohecatonicosidishexacosachoron alterprism3.855219
stut pixady4Dsmall tritrigonal prismatohexacosidihecatonicosachoron3.835128
stut thix4Dsmall tritrigonal trishecatonicosihexacosachoron3.835128
stut xethi4Dsmall tritrigonal hexacositrishecatonicosachoron3.835128
stuttixady4Dsmall tritrigonary hexacosidishecatonicosachoron3.835128
suph7Dsmall petated hexadecaexon, hexicated octaexon, expanded octaexon,lattice A7 contact polytope (span of its roots), equatorial cross-section ofoca-firstsoxeb, equatorial cross-section ofroc-firstrek1
suposaz7Dsmall petated hepteractihecatonicosoctaexon, hexicated hepteract1.719624
suthesa7Dsmall terated demihepteract, hexic hepteract1.369306
suti4Dsmall tetrakisicositetrachoron1.608038
sutia5Dsmall-tetrakisicositetrachoron alterprism1.677756
swav ditathi4Dsmall sphenoverted ditrigonary triakishecatonicosachoron2.572554
swavathi4Dsmall sphenoverted triakishecatonicosachoron2.093315
swavixady4Dsmall sphenoverted hexacosadishecatonicosachoron3.294556
...2Dsnub of hyperbolic[10,8,4,6] tiling with tetragonal Coxeter domain

T

...3Dpyritohedallyexpandedicosidodecahedron
...3Drhombical dodeca-augmentedsnub-dodecahedral variant, rhombi-propello-icosahedron
...3Dicosa-expandedrhombic enneacontahedron
...3Drhombical octa-augmentedtruncated-octehedral variant
...3Dexpanded octa-augmentedtruncated-octehedral variant
...3Drhombical hexa-augmentedsnub-cubical variant, rhombi-propello-octahedron
tabatch3Dtruncatedbitruncated-cubic-honeycomb
tabene4Dtrigonal-bipyramidal enneacontahexachoron, joined icositetrachoron,rectified-icositetrachoron dual, surtegmated icositetrachoron
tabif8Dtruncateddiacositetracont-dischiliahectohexaconta-zetton5.830952
tac5Dtriacontiditeron,pentacross (β5), aeropet(id),pentachoral antiprism,vertex figure ofgee,Gosset polytopes 21,1,lattice C5 contact polytope (span of its small roots), equatorial cross-section of vertex-firstgee0.707107
taccarat6Dtriacontaditeron atoprectified triacontaditeron,tac-firstrotunda ofrectified hexacontitetrapeton, rectifiedtriacontaditeron-pyramid1
taccasc7Dtriacontiditeronscalene, half ofhexacontitetrapeton pyramid, quarter ofhecatonicosoctaexon0.707107
taccete8Dtriacontiditerontettene0.707107
taccup6Dtriacontiditeron prism,vertex figure ofrez0.866025
taccuppy7Dtriancontaditeron-prism pyramid, vertex pyramid ofrectified hecatonicosoctaexon1
tacog6Dtericellatedhexacontitetrapeton, pentitruncatedhexeract3.121320
tacogral (old: gatocral)6Dtericelligreatorhombatedheptapeton, pentistericantitruncated heptapeton2.976095
tacox6Dtericellatedhexeract, pentitruncated hexacross2.474130
tacpy6Dtriacontaditeric pyramid, vertex-firstrotunda ofgee0.707107
tacpyp7Dtriacontaditeric-pyramid prism, edge-firstrotunda ofgeep0.866025
tactaf6Dtericellitruncatedtetradecapeton, pentisteritruncatedheptapeton2.236068
tacu6Dtac-based ursapeton,vertex figure of s3s4o3o3o3o4o1.144123
tacytatoh (old: tabtatoh)3Dtruncatedcyclotruncated tetrahedral-octahedral honeycomb (truncatedbitruncated tetrahedral-octahedral honeycomb)
tadeca4Dtruncateddecachoronsqrt(2y2+7y+7)
tag6Dtruncatedhexacontitetrapeton, equatorial cross-section ofgee-firsttaz1.581139
taggix4Dtruncated grand hexacosachoron1.199039
taghi4Dtruncated grand hecatonicosachoron3.477092
tagopal (old: gatopal)6Dterigreatoprismatedheptapeton, pentiruncicantitruncated heptapeton3.116775
tagyrid, J743Dtrigyrated rhombicosidodecahedron2.232951
tah4Dtesseractihexadecachoron, bitruncatedtesseract, bitruncatedhexadecachoron, runcicantic tesseract2.121320
..., tah || grit5D(degenerate)tah atopgrit∞   i.e. flat in euclidean space
taha (old: tahagtah), tah || gyro tah5Dtah alterprism,tah atop gyrotah2.150581
tahatico5Dtah atoptico,tah-first segment ofpirt3
tahgyt6Dtesseractihexadecachoricgyrotrigonism2.160247
tahi4Dtriakishecatonicosachoron2
tahp5Dtesseractihexadecachoron prism, bitruncated-tesseract prism, bitruncated-hexadecachoron prism2.179449
take10Dtruncated chilliaicositetraxennon, truncated decacross1.581139
taki3Dtruncated chiro-icosahedron,compound of 5tut1.172604
takus7Dteriskewed hepteract1.658312
talq7Dtruncatedpentacontihexapentacosiheptacontihexaexon2.645751
tan5Dtruncatedpenteract2.465447
tanoh5Dtruncated penteractic pentacomb
tanq7Dtruncated hecatonicosihexapentacosiheptacontihexaexon2.179449
taope5Dtriangle atopoctahedral-prism,trip atop gyro-paratriddip0.866025
tapech3Dhyperbolic truncated alternated order-5 cubic honeycomb, hyperbolic cantic order-5 cubic honeycomb1.841352i
taporf (old: staporf)6Dteriprismatorhombitetradecapeton, pentiruncicantellatedheptapeton2.449490
tapox (old: stapox)6Dteriprismatedhexeract, penticantellated hexacross2.707107
tar (old: harie)3Dtruncated rhombihedron, hyperhombicosicosahedron,compound of 5tic1.778824
targi3Dtrireplenished great icosahedron0.587785
tark8Dtrirectified diacosipentacontahexazetton1.414214
tarn9Dtrirectified enneract, trirectified octadecayotton1.732051
tarv9Dtrirectified pentacosidodecayotton1.414214
tasa7Dtruncated hepteract2.998773
tasquat2Dhyperbolic truncated infinite-order square tiling1.098684i
tassiph3Dtruncated square prismatic honeycomb
tastic4Dtruncatedstellated tetracontoctachoron,compound of 2truncated icositetrachora2.645751
tat4Dtruncatedtesseract2.149726
..., tat || grit5D(degenerate)tat atopgrit∞   i.e. flat in euclidean space
..., tat || prit5D(degenerate)tat atopprit∞   i.e. flat in euclidean space
tatoh3Dtruncated tetrahedral-octahedral honeycomb, truncated alternated cubic honeycomb, cantic cubic honeycomb
tatraffip6Dtriangle atoptraffip0.925820
tatriddip4Dtruncatedtriangular duoprismsqrt[(2y2+5y+5)/3]
tatsa7Dtritruncated hepteract2.915476
tattip5Dtruncated-tesseract prism2.207107
tattit4Dtruncated tesseractic tetracomb
tattoc7Dtritruncated octaexon1.854050
tau ope4Dtetra-augmentedope
tau tope4Dtetra-augmentedtope
taud, J613Dtriaugmented dodecahedron
tauhip, J573Dtriaugmented hexagonal prism
tautid, J713Dtriaugmented truncated dodecahedron
tautip, J513Dtriaugmented trigonal prism
tautipip4Dtriaugmented-triangular-prism prism
tautisdip4Dtriaugmented3,4-duoprism...
taz7Dtruncated hecatonicosoctaexon, truncated heptacross, equatorial cross-section ofzee-firsttek1.581139
tazat2Dhyperbolic truncated order 3 horocyclic tiling, hyperbolic truncated order 3 apeirogonal tiling1.936492i
tazt2Dhyperbolic trigonal-horocyclic tiling, hyperbolic triapeirogonal tiling1i
taztrat2Dhyperbolic truncated order ∞ trigonal tiling1.414214i
te3Dtruncated icosiicosahedron,compound of 10tut1.172604
teday9Dtruncated decayotton1.431782
teddi adoe, teddi || doe, K-4.834Dtridiminished-icosahedron atopdodecahedron, triminished segment of vertex-firsthexacosachoron1.618034
teddi aid, teddi || id, K-4.1474Dtridiminished icosahedron atopicosidodecahedron3.077684
teddi, J633Dtridiminished icosahedron, ursahedron,vertex figure ofsadi0.951057
teddipe4Dtridiminished-icosahedron prism1.074481
teddipy, K-4.884Dtridiminished-icosahedral pyramid1.618034
teddoe3Dtetrahedrally diminisheddodecahedron,vertex figure ofpd{3,5,3}1.401259
teddot5Dtetradiminisheddodecateron,bidrap alterprism,bidrap atop gyroinvertedbidrap0.866025
tedhin5Dtetradiminishedhemipenteract, square ||hex0.790569
tedjak (alt.: hexgyt, hexalhin)6Dtridiminished icosiheptaheptacontidipeton, tridiminished 22,1,hexadecachoralgyrotrigonism0.816497
tedope4Dtetra(hedrally) diminishedoctahedronal prism0.866025
tedrag6D(cyclo-)tetra-diminishedrag1
tedrat5D(cyclo-)tetra-diminishedrat1
tedrid, J833Dtridiminished rhombicosidodecahedron, magnaursahedron2.232951
tedrix5Dtridiminishedrectified hexateron, square triorthowedge,lace simplex of 3 mutually orthogonal squares0.816497
tedroc7Dtetradiminishedrectified octaexon, (hix,hix,tedrix)-trigonic0.866025
tehat2Dhyperbolic tetrahexagonal tiling1i
tehipau tuttip4Dhip-wise tetra-augmentedtuttip
tehtrah (old: datha)3Dtetrahemitriangular honeycomb, ditetratihemiapeiratic honeycomb
tek8Dtruncated diacosipentacontahexazetton, truncated octacross, equatorial cross-section ofek-firsttiv1.581139
tekah3Dtetrakis hexahedron, apiculated cube
telex4Dvertex first tele-elongatedhexacosachoron
ten9Dtruncated enneract3.450631
tene8Dtruncated enneazetton1.414214
teoct2Dhyperbolic tetraoctagonal tiling0.840896i
tepaco (alt.: tettet cotric)5Dtepe atopco, 0.217953-luna ofscad, (tet,tet,co)-trigonic, partialStott expansion ofhix1
tepacube5Dtepe ||cube,bidrap prism, bi-edge-dimin.rappip, wedge-facetedrappip0.921954
tepasc6Dtetrahedral-prismaticscalene,tetrahedron-prism-pyramid pyramid, line atop fully orthogonaltetrahedron prism0.866025
tepatut (alt.: tettet tuttric)5Dtepe atoptut,tepe-first wedge ofsiphin, (tet,tet,tut)-trigonic1.274755
tepcus3Dtetrapod-cut-sirco1.398966
tepdid3Dtripentadiminished icosidodecahedron1.618034
tepe, K-4.9 (alt: dycuf)4Dtetrahedron prism, line ||trip, square - square bi-wedge, digonal orthobicupolaic ring,vertex figure ofrix, dyadiccupolafastegium, equatorial cross-section oftet-firsthin0.790569
tepeacope5Dtepe atopcope,tepe-first half ofspiddip1.118034
tepeatuttip5Dtepe atoptuttip,tetatut-prism1.322876
tepepy5Dtetrahedral-prismatic pyramid, vertex pyramid ofrectified hexateron0.816497
tepepyp6Dtetrahedral-prismatic pyramid prism, prism oftepepy0.957427
tepet (old: tepeat)2Dhyperbolic tetrapentagonal tiling1.272020i
teppix (old: dattix)4Dtripesic hexacosachoron,compound of 60deca1.414214
terjakh6Dtetrarectified icosiheptaheptacontidipetic hexacomb
teru10Dtetrarectified hendecaxennon, quadrirectified hendecaxennon,Gosset polytope 05,41.167748
tes (alt.: squadip), K-4.204Dtesseract, octachoron, "hypercube", 4Dmeasure-polytope (γ4), 8-cell, geoter(id), square duoprism,vertex figure oficot1
..., tes || sadi5Dtes atopsadi∞   i.e. flat in euclidean space
..., tes || srit5D(degenerate)tes atopsrit∞   i.e. flat in euclidean space
tespy5D(degenerate)tes pyramid∞   i.e. flat in euclidean space
tessap5Dtesseract antiprism,hexadecachoron antiprism1.050501
tessarit5Dtesseract atoprectified tesseract1.227160
test4Dtesseractic tetracomb, 4Dhypercubical honeycomb (δ4),Voronoi complex of C4lattice,Delone complex of C4lattice
tet3Dtetrahedron, 3Dsimplex (α3), pyrochor(id), regular trigonal pyramid, digonal antiprism, regular (di)sphenoid, hemicube, smaller Delone cell of face-centered cubic (fcc)lattice, regular line-scalene, regular (point-)tettene,vertex figure ofpen,Gosset polytope 02,Waterman polyhedron number 1 wrt. face-centered cubiclattice A3 centered at a shallow hole0.612372
...5Dhex atopoctaco,rap atop alt.tetaco, 0.323792-lune ofrat,tet-firstlune ofrat, (oct,tet,dualtet,co)-cyclelace ring1
tet-gybef7Dtet-gyrobifastegium,tet atoptetdip atop perpendiculartet...
teta ope (alt.: octarap, tetoct octtric)5Dtetrahedron atopoctahedron-prism,octahedron atoprectified-pentachoron, half ofdodecateron (itstet-firstrotunda), (tet,oct,oct)-trigonic0.866025
teta troct6Dtetrahedron atoptriangle-octahedron duoprism0.925820
teta tuttip (alt.: tettut tuttric)5Dtet atoptuttip,tet-first cap ofsirhin, (tet,tut,tut)-trigonic1.620185
tetacho4Dtetrahedron atopcubohemioctahedron1
tetaco altepetric6D(tetaco,tepe)disphenoid, (tetaco,tepe) duopyramid, (tet,co, invtepe)trigonic, (tet,tet, dualtet,co)tetrahedric1
tetaco altut4Dtetrahedron atopcuboctahedron atop invertedtruncated tetrahedron...
tetaco ausrip4Dtetaco-augmentedsrip
tetaco, tet || co, K-4.234Dtetrahedron atopcuboctahedron,tetrahedralrotunda ofsmall prismatodecachoron1
tetacoa cube4Dtetrahedron atopcuboctahedron atopcube...
tetacoaoct4Doctahedron atop (pseudo)cuboctahedron atoptetrahedron1
tetacope5Dtet atopcope,tet-first segment ofspix1.190238
tetaf (alt.: tetaltepe, tettet altettric)5Dtetrahedral antifastegium,tet atop invertedtepe,tet-firstrotunda ofhin, (tet,tet,dualtet)-trigonic0.790569
tetafip6Dprism oftetrahedralantifastegium,tetaf prism,tepe atop invertedsquatet, half ofhinnip0.935414
tetal tetdip7Dtet atop dualtetdip0.935414
tetal tratet6Dtetrahedron atop alternatetriangle,tetrahedron-duoprism0.866025
tetaltut, tet || inv. tut4D(degenerate)tetrahedron atop invertedtruncated tetrahedron, (degenerate)tetrahedron atop alternatetruncated tetrahedron∞   i.e. flat in euclidean space
tetaopepy6Dteta ope pyramid,tet atopopepy,pen atopope1
tetatricu, tet || tricu, K-4.244Dtetrahedron atoptrigonal cupola, 0.290215-luna ofsmall prismatodecachoron1
tetatut, K-4.564Dtetrahedron atoptruncated tetrahedron,tetrahedral cap ofrectified tesseract1.224745
tetco6Dtetrahedron-cuboctahedron duoprism1.172604
tetco tuttric5D(tet,co,tut)-trigonic1.274755
tetcube6Dtetrahedron - cube duoprism1.060660
tetcubedaw (alt.: daworsquip)5D(tet,cube)-disphenoid, (tet,cube)-duopyramid, 1/6-lune ofdodecateron,digonal antiprism atop axis-orthogonalsquare prism0.866025
tetdip6Dtetrahedron-tetrahedron duoprism,vertex figure ofhe0.866025
tetdippa octdip7Dtetrahedral-duoprism atopoctahedral-duoprism, vertex-first subsegment of thehexadecaexon1
tetdippy7Dtetdip pyramid, vertex pyramid ofhe1
tetdoe6Dtetrahedron-dodecahedron duoprism1.529224
tete (old: tedpy)4D(line-)tetrahedron-tegum, tetrahedral bipyramid
tetgittith7D(tet,gittith)-duoprism1.080691
tetgocco6D(tet,gocco)-duoprism0.958067
tethex7Dtetrahedron - hexadecachoron duoprism,vertex figure oftark0.935414
tethex aico8Dtethex atopico1
tethin8Dtetrahedron -hemipenteract duoprism,vertex figure of trigoh1
tethix8Dtetrahedron-hexateron duoprism,vertex figure oftreday0.889757
tethop9Dtetrahedron-heptapeton duoprism,vertex figure oftru0.896421
tetid6Dtetrahedron-icosidodecahedron duoprism1.730039
tetike6Dtetrahedron-icosahedron duoprism1.131154
tetoct6Dtetrahedron-octahedron duoprism,vertex figure ofsez0.935414
tetocta7Dtetrahedron-octahedron-duoprismaticalterprism,tet-first medial segment ofbroc0.968246
tetpen7Dtetrahedron-pentachoron duoprism,vertex figure oftrene0.880341
tetrap7Dtetrahedron - rectified-pentachoron duoprism,vertex figure oftorfy0.987421
tetrappal octrap8D(tetrahedron, rectified pentachoron)-duoprism atop alternate(octahedron, rectified pentachoron)-duoprism1.054093
tetripau tuttip4Dtrip-wise tetra-augmentedtuttip
tetrit7Dtetrahedron -rectified-tesseract duoprism1.369306
tetsocco6D(tet,socco)-duoprism1.527124
tetsrip7Dtetrahedron -small-rhombated-pentachoron duoprism0.987421
tetsteth7D(tet,steth)-duoprism1.606894
tettac8Dtetrahedron-triacontiditeron duoprism,vertex figure oftarv0.935414
tettepe7Dtetrahedron-tetrahedron duoprismatic prism,vertex figure of03,3,11
tettes7Dtetrahedron-tesseract duoprism1.172604
tettidjak6Dtruncation oftridiminished icosiheptaheptacontidipeton2.449490
tettut6D(tetrahedron,truncated-tetrahedron)-duoprism1.322876
tetu4Daxially-tetrahedral ursachoron ofx3xoo3ooo&#xt,tet-basedursulate,vertex figure ofsadit1
tewau thawrorh4Dtetra-augmentedthawro rhombochoron...
tex4Dtruncatedhexacosachoron4.643523
..., tex || sidpixhi5D(degenerate)tex atopsidpixhi∞   i.e. flat in euclidean space
texip5Dtruncated-hexacosachoron prism4.749980
tezt2Dhyperbolic tetragonal-horocyclic tiling, hyperbolic square-apeirogon tiling0.707107i
tha2Dtrigonal hemiapeirogonal tesselation
thah3Dtetrahemihexahedron,vertex figure oftho, triangular crossedcuploid0.707107
thahp4Dtetrahemihexahedral prism,vertex figure ofrhohid0.866025
thaph3Dtruncated-hexagonal prismatic honeycomb
thaquitoth4Dtesseractihexadecaquasitruncated tesseractihexadecachoron1.338990
thaquitpath4Dtesseractihexadecaquasitruncated prismatotesseractihexadecachoron1.608038
that2Dtrihexagonal tiling, Kagomé tiling
thatap0Dtriangular-hexagonal tiling antiprism
thatgyt4Dtriangular-hexagonal tilinggyrotrigonism
thatoth4Dtesseractihexadecatruncated tesseractihexadecachoron1.790840
thatpath4Dtesseractihexadecatruncated prismatotesseractihexadecachoron2.326846
thattip3Dtrihexagonal tiling prism
thawro, J923Dtriangular hebesphenorotunda
...4Dthawro pyrite, octa-diminishing ofid -srid - F-ike -ti tower...
...4Dthawro wedge...
thawrorh4Dthawro rhombochoron...
...4Dthawro-wedged 1/6-luna ofhexacosachoron...
...4Dthawro-wedged 2/6-luna ofhexacosachoron...
thax6Dtruncatedhemihexeract, cantichexeract2.179449
thaxa7Dthax alterprism, medial segment ofsirhesa2.207940
theat2Dtruncated heptagonal tiling, hyperbolic order 3 truncated heptagonal tiling3.792295i
thenne9Dtruncatedhemienneract, canticenneract2.850439
thesa7Dtruncateddemihepteract, cantichepteract2.423840
thet2Dhyperbolic triheptagonal tiling2.012192i
thetrat2Dtruncated order 7 triangular tiling, hyperbolic order 7 truncated trigonal tiling2.976586i
thex4Dtruncatedhexadecachoron, cantictesseract, equatorial cross-section ofhex-firsttot1.581139
..., thex || prit5D(degenerate)thex atopprit∞   i.e. flat in euclidean space
thexa (old: thexag thex), thex || gyro thex5Dthex alterprism,thex atop gyrothex, equatorial segment ofsirhin1.620185
thexagtah5Dthex atop gyratedtah2.371708
thexarico5Dthex atoprico,ico-first subsegment ofsart1.732051
thexatah5D(degenerate)thex atoptah∞   i.e. flat in euclidean space
thexgyt (alt.: pex tedjak)6Dtruncated-hexadecachoralgyrotrigonism, partially expandedtridiminished icosiheptaheptacontidipeton, partially expanded tridiminished 21,21.632993
thexip5Dtruncated-hexadecachoron prism1.658312
thext4Dtruncated hexadecachoric tetracomb, truncated demitesseractic tetracomb, cantic tesseractic tetracomb
thi4Dtruncatedhecatonicosachoron8.218334
thiddip, K-4.474Dtriangle - hexagon duoprism, hexagon -hip wedge1.154701
thidlaq (alt.: trarixdap)7Dtriaconta-hexa-diminishedpentacontihexapentacosiheptacontihexaexon, triangular-rectified-hexatericduoalterprism1
thihexat2Dhyperbolic truncated order 6 hexagonal tiling1.221076i
thin5Dtruncatedhemipenteract, canticpenteract1.903943
thina6Dthin alterprism, medial segment ofsirhax1.936492
thinoh5Dtruncated hemipenteractic pentacomb
thipe5Dtruncated-hecatonicosachoron prism8.233530
thiph3Dtriangular-hexagonal prismatic honeycomb
thisquat2Dhyperbolic truncated order 6 square tiling1.632242i
tho4Dtesseractihemioctachoron, octahemioctachoron,vertex figure ofhehad0.707107
thocto8Dtruncatedhemiocteract, canticocteract2.645751
thon3Dhyperbolic order 6tetrahedral honeycomb0i
thoot thibbit4Dtomohexagonal-omnitruncated-trihexagonal duoprismatic tetracomb
thorahbit4Dtomohexagonal-rhombitrihexagonal duoprismatic tetracomb
thot thibbit4Dtrihexagonal-omnitruncated-trihexagonal duoprismatic tetracomb
thotithit2Dtrihexagonaltruncated trihexagonal tiling
thox (old: thod)6Dtriacontidiahemihexeract, triacontidihemidodecapenton, cytohemiectid,vertex figure ofguhsa0.707107
thrathibbit8Dtrihexagonal-rhombitrihexagonal duoprismatic tetracomb
ti3Dtruncatedicosahedron, buckyball, Goldberg polyhedron GP(1,1)2.478019
tiatid, ti || tid, K-4.1514Dtruncated icosahedron atoptruncated dodecahedron3.835128
tibbic4Dtriangular-bipyramidal chilliadiacosichoron,rectified-hecatonicosachoron dual, surtegmated hexacosachoron
tibbid (alt.: durap)4Dtriangular-bipyramidal decachoron,rectified-pentachoron dual, surtegmated pentachoron, joined pentachoron
tibbit4Dtriangular-bipyramidal triacontadichoron,rectified-tesseract dual, surtegmated hexadecachoron
tic3Dtruncatedcube, truncated hexahedron1.778824
...2Dinfinite polyhedron from alternatingtic/tut structure
...4Dexpanded augmented axially-octahedral ursachoron ofx3xoo4xxx&#xt
tica gircobcu4Dticagirco bicupola
ticagirco, K-4.1284Dtruncated cube atopgreat rhombicuboctahedron,truncated-cubical cap ofprismatorhombated hexadecachoron,cuboctahedral supra-cap ofsmall rhombated icositetrachoron2.613126
ticca gircope5Dtruncated-cube atopgreat-rhombicuboctahedron-prism3.239235
ticca sircope5Dtruncated-cube atopsmall-rhombicuboctahedron-prism1.914214
ticcup, K-4.994Dtruncated-cube prism1.847759
tich3Dtruncated cubic honeycomb
tico4Dtruncatedicositetrachoron, cantitruncatedhexadecachoron2.645751
..., tico || gidpith5D(degenerate)tico atopgidpith∞   i.e. flat in euclidean space
..., tico || gyro prico5D(degenerate)tico atop gyratedprico∞   i.e. flat in euclidean space
..., tico || prissi5Dtico atopprissi2.647378
ticont4Dtruncatedtetracontoctachoronsqrt[(6+4 sqrt(2))y2+(23+16 sqrt(2))y+(23+16 sqrt(2))]
ticope5Dtruncated-icositetrachoron prism2.692582
ticot4Dtruncated icositetrachoric tetracomb
tid3Dtruncateddodecahedron2.969449
...4Dexpanded augmented axially-icosahedral ursachoron ofxo3xooo5xxxx&#xt
...4Dtriaconta-sphenatedid-first tristratic sub-cap ofrahi...
tidagrid, tid || grid, K-4.1734Dtruncated dodecahedron atopgreat rhombicosidodecahedron,truncated-dodecahedral cap ofprismatorhombated hexacosichoron9.744610
tiddip, K-4.1304Dtruncated-dodecahedron prism3.011250
tiddoh3Dhyperbolic truncated (order 4) dodecahedral honeycomb2.246127i
tidect2Dhyperbolic tri-decagonal tiling1.272020i
tidimex (alt.: idimtex)4Dtruncatedicosidiminished hexacosachoron, icosidiminishedtruncated hexacosachoron4.643523
tidox (old: togex)4Dtruncated dodecahedronary-hexacosachoron (truncated great hexacosachoron),compound of 25tico2.645751
tidril6Dtridiminishedrectified heptapeton, (pen,pen,bidrap)-trigonic0.845154
tidtes4Dtetra-diminished tesseract1
tidtidohi4Dtruncated ditrigonary dishecatonicosachoron2.645751
tiduro4Dtruncated dodecahedronal ursarotunda3.077684
tiffix4Dtruncated faceted hexacosichoron4.643523
tiffy8Dtruncated dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton2.645751
tifipte4Dhyperbolic order 5 faceted-hexacosichoral tetracomb, hyperbolic order 5 icosahedral-hecatonicosachoral tetracomb, hyperbolic ridged pentachoric tetracomb, terifaceted hyperbolic pentachoric tetracomb0.393076i
tigaghi4Dtruncated great grand hecatonicosachoron2
tigfix4Dtruncated great faceted hexacosichoron1.199039
tiggia gaquatid4Dtruncated great icosahedron atopgreat quasitruncated icosidodecahedron1.120533
tiggidtixhi4Dtruncated great ditrigonary hexacosihecatonicosachoron2.645751
tiggipe4Dtruncated-great-icosahedron prism1.165943
tiggy3Dtruncatedgreat icosahedron, great truncated icosahedron1.053292
tighi4Dtruncated great hecatonicosachoron3.477092
tigid3Dtruncatedgreat dodecahedron1.876844
tigiddip4Dtruncated-great-dodecahedron prism1.942303
tigikaike4Dtruncatedgikaike2.645751
tih3Dhyperbolic truncated order 3 icosahedral honeycomb2.082108i
tijakdap (alt.: kehdfy)8Dtriangle-icosiheptapeticduoalterprism, heptacontadia-hexa-diminisheddischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton1
tikit3Dtriakis tetrahedron, apiculated tetrahedron
tikko3Dtriakis octahedron, apiculated octahedron
til6Dtruncatedheptapeton1.362771
tim6Dtruncatedpentacontitetrapeton2.645751
tin5Dtriacontadipenteract1.414214
...4Dvertex figure oftriacontadipenteract0.935414
tip (alt: tettum)4Dtruncatedpentachoron,tet-basedtutsatope,tet-based tutism1.264911
tipadeca5Dtip atopdeca, 2nd segment ofrin inpen-first orientation1.414214
tipagrip5Dtip atopgrip2.150581
tipalprip5Dtip atop invertedprip1.632993
tipaprip, tip || prip5D(degenerate)tip atopprip∞   i.e. flat in euclidean space
tipe, K-4.1274Dtruncated-icosahedron prism2.527959
tipech3Dhyperbolic truncated order 5 cubic tesselation1.734413i
tiph3Dtriangular prismatic honeycomb,Delone complex of unit-stacked hexagonallattice
tipped3Dhyperbolic truncated order 5 dodecahedral honeycomb1.383373i
tippip5Dtruncated-pentachoron prism1.360147
tiquithdow6D(triangle,quith)-disphenoid, (triangle,quith)-duopyramid, triangle atop fully orthogonalquasitruncated hexahedron0.645976
tirjakdap8Dtriangle-rectified-icosiheptapeticduoalterprism1.414214
tisadi (alt.: idtex)4Dtruncatedsnub icositetrachoron, icositetradiminishedtruncated hexacosachoron4.643523
tiscad5Dtruncatedsmall-cellated-dodecateronsqrt[(3y2+12y+14)/3]
tiscsrix4Dtristraticicosidodecahedron-first cap ofsmall rhombihexacosachoron6.073594
tisdip altratet6Dtisdip atop gyratedtratet0.925820
tisdip, K-4.184Dtriangle - square duoprism, square -cube wedge,vertex figure ofnit0.912871
tisdipah5Dtisdip atop hexagon1
tisdippy5Dtriangle-square-duoprism pyramid, vertex pyramid ofnit1.224745
tispic4Dtruncatedsmall prismated tetracontoctachoronsqrt[(2+sqrt(2))y2+(7+4 sqrt(2))y+(7+4 sqrt(2))]
tispid4Dtruncatedsmall prismated decachoronsqrt(y2+3y+3)
tisquah3Dhyperbolic trancatedsquare-tiling honeycomb2.030104i
tisquippy5Dtriangle-squippy douprism, half oftroct, (triangle,trip,trip)-trigonic0.912871
tissidtixhi4Dtruncated small ditrigonary hexacosihecatonicosachoron2.645751
tissish3Dhyperbolic truncated order 4square-tiling honeycomb1.098684i
tisso3Dtruncated stella octangula,compound of 2tut1.172604
tistadip4Dtriangle - pentagram duoprism, pentagram -stip wedge0.780850
tisted4Dtruncatedstellated decachoron,compound of 2truncated pentachora1.264911
tisthit4Dtriangular-simotrihexagonal tetracomb
tistodip4Dtriangle - octagram duoprism, octagram -stop wedge0.791345
titajak (old: totajik, oldest: hibtajak)6Dtritruncatedicosiheptaheptacontidipeton, (demibitruncatedicosiheptaheptacontidipeton)3.829708
titam (old: cacram, totam, tomak, katom)6Dtritruncatedpentacontitetrapeton, (centrocellirhombated pentacontitetrapeton, trunkated pentacontitetraheptacontidipeton, heptacontiditruncated pentacontitetrapeton)3.741657
titanoh5Dtritruncated penteractic pentacomb,Voronoi complex of body-centered penteracticlattice (lattice D5*)
titch3Dhyperbolic x3x3o3x4*a tesselation, truncated tetrahedral-cubic honeycomb2.256021i
titdi3Dtri-trigonally diminishedicosahedron, (subsymmetrically) tristellated-dodecahedron, tri-kis-dodecahedron, dual ofteddi,vertex figure oftridex
titdoh3Dhyperbolic x3x3x3o4*a tesselation, truncated tetrahedral-disoctahedral honeycomb2.085865i
titepe4Dtruncatedtetrahedral prismsqrt[(5y2+12y+12)/8]
tithah3Dtruncatedtetrahemihexahedron1.581139
titho4Dtruncated tesseractihemioctachoron1.581139
tithtip6Dtriangle-triangle-hexagon triprism1.290994
titraf6Dtriangle-traf duoprism0.966092
titridafup7Dtriangle-tridafup duoprism1.040833
titrip3Dtruncatedtriangular prism, expandedambified tripsqrt[(7y2+16y+16)/12]
titstip6Dtriangle-triangle-square triprism1.080123
titwadip4Dtriangle - dodecagon duoprism, dodecagon -twip wedge2.016280
tiv9Dtruncated pentacosidodecayotton, truncated enneacross, equatorial cross-section ofvee-firsttake1.581139
tix (alt.: pentum)5Dtruncatedhexateron,pen-basedtutism1.322876
tixip6Dtruncated-hexateron prism1.414214
toa sircope5Dtruncated-octahedron atopsmall-rhombicuboctahedron-prism1.583946
toagirco, toe || girco, K-4.1494Dtruncated octahedron atopgreat rhombicuboctahedron,truncated octahedral cap ofprismatorhombated icositetrachoron3.498949
toagircoatic4Dtoe atopgirco atoptic
toatic, toe || tic, K-4.984Dtruncated octahedron atoptruncated cube1.785406
tobcu, J273Dtriangular orthobicupola,vertex figure ofgytoh1
tobcuatut, tobcu || tut, K-4.494Dtriangular-orthobicupola atoptruncated-tetrahedron1.183216
tobcupe, K-4.444Dtriangular-orthobicupola prism1.118034
toby (old: tobay)8Dtruncated diacositetracont-myriaheptachiliadiacosioctaconta-zetton4
toc7Dtruncated octaexon1.391941
tocal6Dteracellatedheptapeton, pentitruncated heptapeton1.647509
tocap4Dtoroidal cycloantiprism1
tocat2Dhyperbolic order 3 truncated octagonal tiling2.947161i
tocral (old: stocral)6Dtericellirhombatedheptapeton, pentiruncitruncated heptapeton2.329929
tocrax (old: stocrax)6D(small) tericellirhombatedhexeract, pentiruncitruncated hexacontitetrapeton3.734936
toct2Dhyperbolic trioctagonal tiling1.553774i
tocth3Dhyperbolic truncated (order 4) octahedral honeycomb1.414214i
tocto8Dtruncated octeract3.232607
todin5Dtriacontadiadispenteract,compound of 2hin0.790569
todip, K-4.594Dtriangle - octagon duoprism, octagon -op wedge1.428440
todithix4Dtoroidoditrigonary hecatonicosihexacosichoron1.732051
todtixhi4Dtoroidal ditrigonal hexacosihecatonicosachoron1.732051
toe (alt.: gratet)3Dtruncatedoctahedron, omnitruncatedtetrahedron, great rhombitetratetrahedron, Voronoi cell of body-centered cubic (bcc)lattice, Kelvin's tetrakaidecahedron,Waterman polyhedron number 10 wrt. face-centered cubiclattice A3 centered at a lattice point,permutohedron of 4 elements, equatorial cross-section ofoct-firstthex1.581139
toedip6Dtruncated-octahedron - truncated-octahedron duoprism2.236068
toegippid7Dtruncated-octahedron -great-prismated-decachoron duoprism2.738613
togdow5Dtriangle-octagrammic disphenoid, triangle-octagrammic duopyramid, triangle atop fully orthogonal octagram0.638475
togral (old: gotral)6Dterigreatorhombatedheptapeton, penticantitruncated heptapeton2.390457
togrig (old: gotrig)6Dterigreatorhombihexacontitetrapeton, (old: great terirhombated hexacontatetrapeton), penticantitruncated hexacontitetrapeton3.569684
toif3Dtoroidal icosahedron faceting,edge facetingike-6-6-a, crazy tube0.951057
tojak6Dtruncatedicosiheptaheptacontidipeton2
tolin7Dtruncatedpentacontihexahecatonicosihexaexon3.708099
topag (old: stopag)6Dteriprismatedhexacontitetrapeton, penticantellatedhexeract2.921564
topal (old: stopal)6Dteriprismatedheptapeton, penticantellated heptapeton1.690309
topax5Dpteroprismated hexateron1.190238
...4Dvertex figure oftopax0.907485
topazat2Dhyperbolic truncated order 5 apeirogonal tiling1.130426i
tope, K-4.894Dtruncated-octahedron prism1.658312
topeat2Dhyperbolic order 4 truncated pentagonal tiling2.246127i
topepat2Dhyperbolic truncated order 5 pentagonal tiling1.548400i
topesquat2Dtruncated order 5 square tiling, hyperbolic order 5 truncated square tiling2.113125i
topfu3Dtwo-op-fusion1.398966
torfy8Dtrirectified dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton, t3(41,2)3.162278
...3Dtoroidal pentagrammic bicuploid, star semicupolaic diabolo
...3Dtoroidal tiler
tosot thibbit4Dtomosquare-omnitruncated-trihexagonal duoprismatic tetracomb
tosquat2Dtruncated square tiling
tosquazat2Dhyperbolic truncated order 4 horocyclic tiling, hyperbolic truncated order 4 apeirogonal tiling1.322876i
tot5Dtruncatedtriacontiditeron, truncated pentacross, equatorial cross-section oftac-firsttag1.581139
totaz7Dtritruncatedhecatonicosoctaexon, Voronoi cell oflattice D7*2.549510
totrat2Dtruncated order 8 trigonal tiling, hyperbolic order 8 truncated trigonal tiling2.276396i
totratip3Dhyperbolictruncated order 8 triangle tiling prism2.220806i
tox6Dtruncatedhexeract2.745093
toxat2Dtruncated hexagonal tiling
traco (alt.: cocoe cotric)5Dtriangle -cuboctahedron duoprism, (co,co,co)-trigonic1.154701
tracope6Dtriangle-cuboctahedron duoprismatic prism1.258306
tracube5Dtriangle - cube duoprism1.040833
tracufbil4Dtriangular-cupofastegia biluna, {3} ||tricu || {3}, 0.419569-luna ofgyspid1
traddet4Dtriangular antiditetragoltriatesqrt[(a22+b22)/3]
tradedip, K-4.944Dtriangle - decagon duoprism, decagon -dip wedge1.717954
tradoe5Dtriangle - dodecahedron duoprism1.515539
tradope6Dtriangle-dodecahedron duoprismatic prism1.595888
traf, K-4.64Dtriangular antifastegium, triangleoct wedge, {3} || gyrotrip, {3} ||oct, (vertex-) diminishedrap0.774597
traffip5Dtraf prism,trip atop invertedtisdip0.921954
trafpy5Dtriangular antifastegium pyramid, (triangular prism, gyrotriangular pyramid)-disphenoid0.790569
traginnont7D(triangle,ginnont)-duoprism1.173127
tragirco5Dtriangle - great-rhombicuboctahedron duoprism2.388442
tragittith6D(triangle,gittith)-duoprism1.061238
tragocco5Dtriangle - great-cubicuboctahedron duoprism0.936070
tragrid5Dtriangle - great-rhombicosidodecahedron duoprism3.845977
tragrip6Dtriangle -great-rhombated-pentachoron duoprism1.932184
trah3Dhyperbolic order 3triangle-tiling honeycomb0i
trahex6Dtriangle - hexadecachoron duoprism,vertex figure ofbarz0.912871
trahex aico7Dtrahex atopico1
trahex dafup7Dtriangular-hexadecachoral duoantifastegiaprism,trahex atop dual-gyratedtrahex0.935414
trahexpy7Dtrahex pyramid, vertex pyramid ofbarz1.224745
trahi6Dtriangle - hecatonicosachoron duoprism3.747204
trahin7Dtriangle -hemipenteract duoprism,vertex figure ofborfy0.978945
trahip (old: thiddippip)5Dtriangle hexagonal-prism duoprism, triangle-hexagon duoprismatic prism1.258306
trahix7Dtriangle -hexateron duoprism,vertex figure ofbrene0.866025
trajak8Dtriangle -icosiheptaheptacontidipeton duoprism,vertex figure of bargoh1
trajakdit8D(triangle,jak)-duotegum,tegum product of triangle andicosiheptaheptacontidipeton
traltisdip5Dtriangle atop gyratedtisdip1
...4Dicosaswirlic hexacosachoron, thirtyfold dissectedicosahedral polytwister, thirtyfold dissected ikter...
...4Doctaswirlic enneacontahexachoron, twelvefold dissectedoctahedral polytwister, twelvefold dissected octer1.255926
trapedip, K-4.344Dtriangle - pentagon duoprism, pentagon -pip wedge1.028076
trapen6Dtriangle -pentachoron duoprism,vertex figure ofbroc0.856349
trapen altralrap7Dtriangle-pentachoron duoprism atop bi-invertedtriangle-rectified-pentachoron duoprism1
trapendafup7Dtriangular-pentachoron duoantifastegiaprism,trapen atop bidualtrapen0.866025
trapent7Dtriangle-penteract duoprism1.258306
...3Dtrapezo-rhombic dodecahedron, Voronoi cell of hexagonal close-packing (hcp) "lattice"
trapip (old: trapedippip)5Dtriangle pentagonal-prism duoprism, triangle-pentagon duoprismatic prism1.143215
traquitco5Dtriangle - quasitruncated-cuboctahedron duoprism1.209137
traquith5Dtriangle quasitruncated-cube duoprism0.817997
trarahi6Dtriangle - rectified-hecatonicosachoron duoprism4.571175
trarap6Dtriangle -rectified-pentachoron duoprism,vertex figure ofbranq0.966092
trarapdafup7D(triangle,rectified-pentachoron)-duoantifastegiaprism,pentachoron-first parabidiminishedhexadecaexon1
trarat7Dtriangle -rectified-triacontiditeron duoprism1.154701
trarico6Dtriangle - rectified-icositetrachoron duoprism1.825742
trarit6Dtriangle - rectified-tesseract duoprism1.354006
trarix7Dtriangle-rix duoprism1
trarixdit7D(triangle,rix)-duotegum,tegum product of triangle andrectified hexateron
trarojak8Dtriangle -rectified-icosiheptaheptacontidipeton duoprism1.414214
trarox6Dtriangle - rectified-hexacosachoron duoprism3.131369
trasarx7Dtriangle-rsarxix duoprism1.414214
trashiddip5Dtriangle atopshiddip1.732051
trasinnont7D(triangle,sinnont)-duoprism1.670461
trasirco5Dtriangle small-rhombicuboctahedron duoprism1.513420
trasnic5Dtriangle -snub-cube duoprism1.462497
trasnid5Dtriangle -snub-dodecahedron duoprism2.231808
trasocco5Dtriangle - small-cubicuboctahedron duoprism1.513420
traspid6Dtriangle -small-prismated-pentachoron duoprism1.154701
trasrid5Dtriangle - small-rhombicosidodecahedron duoprism2.306383
trasrip6D(triangle,small rhombated pentachoron)-duoprism1.316561
trasteth6D(triangle,steth)-duoprism1.593876
trat (subsym.: snitititat)2Dtriangular tiling,Delone complex of hexagonallattice A2
tratac7Dtriangle -triacontiditeron duoprism,vertex figure ofbark0.912871
tratah6Dtriangle -tesseractihexadecachoron duoprism2.198484
tratap3Dtriangular tiling antiprism
trateddi, {3} || teddi, K-4.334D{3} atopteddi,teddi based wedge1
tratepe6Dtriangle-tetrahedron-duoprism prism,vertex figure oflanq0.978945
tratess6Dtriangle - tesseract duoprism1.154701
tratet (alt.: tettet tettric)5Dtriangle - tetrahedron duoprism, triangle duofastegium,vertex figure ofbril, (tet,tet,tet)-trigonic0.841625
tratet altroct6Dtriangle-tetrahedron duoprism atop gyratedtriangle-octahedron duoprism, vertex-first medial segment ofbirectified heptapeton0.925820
tratetdafup6Dtriangular-tetrahedral duoantifastegiaprism,tratet atop bidualtratet0.866025
tratetpy6D(triangle,tetrahedron)-duoprism pyramid, vertex-pyramid ofbril0.925820
tratgyt4Dtriangular tilinggyrotrigonism
trathiddip5Dtriangle atopthiddip, triangle-first cap ofsarx1.290994
trati5Dtriangle - truncated-icosahedron duoprism2.544388
tratic5Dtriangle truncated-cube duoprism1.870173
tratid5Dtriangle - truncated-dodecahedron duoprism3.025056
tratoe (alt.: totoe totric)5Dtriangletruncated-octahedron duoprism, (toe,toe,toe)-trigonic1.683251
tratratet7Dtriangle-triangle-tetrahedron-triprism,vertex figure ofGosset polytope03,2,21.020621
tratratrip7Dtriangle - triangle - triangle - triprismatic prism1.118034
tratriddipdit6D(triangle,triangular duoprism)-duotegum,tegum product of triangle andtriangular duoprism
tratrip (old: triddippip)5Dtriangle triangular-prism duoprism, triangle-triangle duoprismatic prism,vertex figure ofram0.957427
trattip3Dtriangular tiling prism
tratut (alt.: tuttut tuttric)5Dtriangletruncated-tetrahedron duoprism, (tut,tut,tut)-trigonic1.307032
traw, K-4.274Dtrigonal antitriwedge, hexagon -octahedral wedge, triangular gyrobicupolaic ring, {6} ||oct, {3} || gyratedtricu, 1/6-luna ofico1
trawp (alt.: opea hip)5Dtraw prism,ope atophip, 1/6-lune oficope1.118034
traxh6Dtri-rectified hexeractic pentacomb,Voronoi complex of body-centered hexeracticlattice (lattice D6*)
trazip3Dxx xw&#q, prism of (isosceles) trapezoid1.306704
treday9Dtrirectified decayotton,Gosset polytope 05,31.095445
trene8Dtrirectified enneazetton,Gosset polytope 04,31.054093
trex6Dtriangle - hexacosachoron duoprism1.717954
trial trahex7Dtriangle atop invertedtrahex1
trial trapen7Dtriangle atop invertedtriangle-pentachoron duoprism, triangle-first cap ofroc0.866025
trial trarap7Dtriangle atop invertedtriangle-rectified-pentachoron duoprism0.992157
trial tratet6Dtriangle atop dualtratet, triangle-first cap ofril0.845154
trial tricupe5Dtriangle atop gyratedtricupe, (triangle,gyrotrip,hip)-trigonic1.224745
trial triddip5D{3} atop gyratedtriddip, {3}-first cap ofrix0.816497
trial troct6Dtriangle atop gyrotroct0.918559
tribbit4Dtriangular duoprismatic tetracomb, triangular biprismated tetracomb,Delone complex of bihexagonallattice A2×A2
trico6Dtriangle -icositetrachoron duoprism1.154701
tricu, J33Dtriangular cupola, half ofcuboctahedron1
tricuatut, tricu || tut, K-4.504Dtriangular-cupola atoptruncated-tetrahedron1.183216
tricuf, K-4.254Dtrigonal cupofastegium, hexagon -triangle-prismatic wedge, triangle orthobicupolaic ring, {6} ||trip, {3} ||tricu, 0.209785-luna ofsmall prismatodecachoron1
tricufip5Dtricuf prism1.118034
tricupe, K-4.454Dtriangular-cupola prism,triangular prism atophexagonal prism1.118034
trid5Dtriangle - icosidodecahedron duoprism1.717954
tridafup (alt.: pabdidot)5Dtriangular duoantifastegiaprism, triangular duoantiwedge,triddip atop bidualtriddip, central segment of vertex firstdot, parabidiminisheddot0.866025
tridafupap7Dtrigonal-duoantifastegiaprismatic alterprism,trigonal-duoantifastegiaprism atop lacing-orthotrigonal-duoantifastegiaprism0.935414
tridafupip6Dtridafup prism1
triddaf5Dtriangular duoantifastegium, digonal-triangular duoantiwedge,trip atop bidualtrip0.790569
triddap4Dtriangle duoantiprism, hemiatedhiddip1.414214
triddep4Dtriangular duoexpandoprism, expandedtriddip,tegum sum of 2 alternatedthiddips1.154701
triddet4Dtriangularditetragoltriatesqrt[(a2+b2)/3]
triddip althiddip5Dtriddip atop gyratedthiddip1.190238
triddip, K-4.104Dtriangle-triangle duoprism, triangle -trip wedge,vertex figure ofdot, Delone cell oflattice A2×A2, equatorial cross-section oftrig-firstrix0.816497
triddipa hip5Dtriddip atophip, (triangle,trip,hip)-trigonic1.190238
triddipabl tratrip6Dtriddip atop bidualtratrip1
triddipasc6Dtriangle-duoprismaticscalene,triangle-duoprism-pyramid pyramid, line atop fully orthogonaltriangle duoprism1
triddippa hiddip5Dtriddip atophiddip,triddip-first cap ofcard1.658312
triddippa tridafup6Dtriddip atoptridafup, ((3,3)-dip, (3,dual 3)-dip, (dual 3,3)-dip)-trigonic0.925820
triddippy5Dtrigonal-duoprismatic pyramid, vertex pyramid of thedodecateron0.866025
triddit4Dtriangle duotegum, dual oftriangle duoprism, 6-2-stepprism0.707107
tridep6Dtriangle-icosidodecahedron duoprismatic prism1.789237
tridex4Dtri-icositetradiminishedhexacosachoron,tetragonal-antiwedge heptacontadichoron1.618034
tridico (alt.: cytid ico)4D(cyclo)tridiminishedico1
tridpy (alt.: trit), J123Dtrigonal dipyramid, (line-)triangle-tegum
tridpyp4Dtriangular-bipyramid prism,tetrahedral prism bicupola, externalblend of 2tetrahedral prisms
trigee8Dtriangle - hexacontitetrapeton duoprism,vertex figure ofbrav0.912871
trihop8Dtriangle - heptapenton duoprism,vertex figure ofbreday0.872872
trike5Dtriangle - icosahedron duoprism1.112583
trikep6Dtriangle-icosahedron duoprismatic prism1.219771
trim (old: cacam, tram, mak)6Dtrirectifiedpentacontitetrapeton, (centrocellated pentacontitetrapeton, pentacontitetraheptacontidipeton)1.414214
trioc9Dtriangle - octaexon duoprism,vertex figure ofbru0.877971
trip, 3-p3Dtriangular prism, digonal cupola, Delone cell of unit-stacked hexagonallattice,vertex figure ofrap0.763763
..., trip || gybef4Dtriangular prism ||gyrobifastegium...
tripa thiddip5Dtrip atopthiddip, (hexagon,trip,hip)-trigonic1.190238
tripal triddip6Dtrip atop gyro-perptriddip0.816497
tripgytricudaw5D(trip, gyrotricu)-disphenoid, (trip, gyrotricu)-duopyramid1
triphipdaw (alt.: tripalhip)5D(trip,hip)-disphenoid, (trip,hip)-duopyramid,trip atop lacing-orthogonalhip1.274755
triphix8Dtriangle - hexateron duoprismatic prism,vertex figure ofribfoh1
trippasc5Dtriangular-prismaticscalene,triangular-prismatic-pyramid pyramid, line atop fully orthogonaltriangular-prism0.790569
trippen7Dtriangle - pentachoron duoprism-prism,vertex figure ofbuffy0.991632
trippepe7Dtrippennene0.866025
trippescu3Dtripod pentagonized semicupola,edge facetingsidtid-0-3-3-30.866025
trippete6Dtriptettene, {3}-first cap ofjak0.816497
trippy, K-4.74Dtrigonal-prismatic pyramid, vertex pyramid of therectified pentachoron0.774597
trippyp5Dtrigonal-prismatic pyramid prism, lacing edge cap of therectified-pentachoron prism0.921954
tript4Dtrigonal-prismatic (line-)tegum,trigonal-prismatic dipyramid...
tripuf, K-4.514Dtrigonal pucofastegium, triangle -hexagon-prismatic wedge, trigonal magnabicupolaic ring, {3} ||hip, {6} ||tricu, {3}-first cap ofsrip1.183216
tripufip (alt.: tripa shiddip)5Dtripuf prism,trip-first cap ofsrippip1.284523
triquip8Dtriangle-triangle-triangle-triangle-tetraprism (or: -quadprism)1.154701
trirp3D(degenerate) trigonal retroprism, retrograde trigonal antiprism∞   i.e. flat in euclidean space
trirp (variant)3Dvertex figure offaceted rectified pentachoron, tallertrigonal retroprism (3/2 antiprism) variant0.763763
trisqdip4Dtrisquare duoprism,compound of 9tes intwaddip army1
tritep (alt: dycufbil)4D(line-)triangle-tegum prism, triangular-bipyramidal prism, dyadic cupofastegia biluna
tritra ope6D(triangle, dual triangle,trip, gyrotrip)lace simplex0.866025
tritricu5Dtriangle-tricu duoprism, half oftraco1.154701
trittip6Dtriangle-triangle-triangle-triprism,vertex figure oframoh1
trizee9Dtriangle - hecatonicosoctaexon duoprism,vertex figure ofbrake0.912871
tro8Dtrirectified octeract, trirectified hexadecazetton1.581139
troct (alt.: octoct octtric)5Dtriangle-octahedron duoprism,vertex figure ofbrag, (oct,oct,oct)-trigonic0.912871
troctal traco6Dtroct atoptraco1.224745
troctpy6Dtroct pyramid, vertex pyramid ofbrag1.224745
trojkoh6Dtrirectified icosiheptaheptacontidipetic hexacomb
trope (old: troctip)6Dtriangle-octahedron duoprismatic prism1.040833
tru10Dtrirectified hendecaxennon,Gosset polytope 06,31.128152
...4Dtruncatedgeneralized Shephard hexadecachoron,complex polychoronop-4-o2-3-x2-3-x2
...3DtruncatedShephard's3-generalised octahedron,complex polyhedronx2-3-x2-4-o3
...3DtruncatedShephard's4-generalised octahedron,complex polyhedronx2-3-x2-4-o4
...3DtruncatedShephard's5-generalised octahedron,complex polyhedronx2-3-x2-4-o5
...3DtruncatedShephard'sp-generalised octahedron,complex polyhedronx2-3-x2-4-op
...3Dcomplex polyhedronx2-4-x3-3-o3
...3DtruncatedHessian polyhedron,complex polyhedronx3-3-x3-3-o3
...4DtruncatedWitting polychoron,complex polychoronx3-3-x3-3-o3-3-o3
...3Dcomplex polyhedronx3-3-x3-4-o2,complex polyhedronx3-3-x3-3-x3
...3Dtruncated3-generalised Shephard cube,complex polyhedronx3-4-x2-3-o2
...3Dtruncated4-generalised Shephard cube,complex polyhedronx4-4-x2-3-o2
...3Dtruncated5-generalised Shephard cube,complex polyhedronx5-4-x2-3-o2
...5Dtruncation oficoap2.816377
...4Dtruncatedhyperbolic o4x4o3*a4x4o3*a tetracomb...
...3Dtruncatedp-generalised Shephard cube,complex polyhedronxp-4-x2-3-o2
...4Dtruncatedgeneralized Shephard tesseract,complex polychoronxp-4-x2-3-o2-3-o2
...3Dtruncatedhyperbolic x4o3o4x4*b tesselation...
tu10Dtruncated hendecaxennon, truncated undecaxennon1.445998
tubidrap4Dblend of 2bidraps0.774597
tucoh3Dhyperbolic x3x4x3o4*a tesselation, truncated cubic-octahedral honeycomb1.599084i
tuhip3Dorthogonalblend ofhexagonal prisms1.118034
tupip3Dorthogonalblend ofpentagonal prisms,vertex figure ofsadsadox0.986715
tuquith3Dblend of 2quasitruncated cubes0.579471
turap4Dtworectified-pentachoroncupolaic blend,vertex figure ofhollow stellated icosatetrachoric antiprism0.774597
tustip3Dorthogonalblend ofpentagagramic prisms,vertex figure ofgadsadox0.725530
tut3Dtruncatedtetrahedron, canticcube,Waterman polyhedron number 2 wrt. face-centered cubiclattice A3 centered at a shallow hole1.172604
...4Dexpanded augmented axially-tetrahedral ursachoron ofxo3xooo3xxxx&#xt
tuta (alt.: pabdirit, tutcup, tutaltut), tut || inv tut, K-4.554Dtruncated tetrahedral alterprism,truncated tetrahedral cupoliprism, runcic snub cubic hosochoron,truncated tetrahedron atop invertedtruncated tetrahedron,truncated tetrahedron atop alternatetruncated tetrahedron,tetrahedrally medial part ofrectified tesseract, parabidiminishedrectified tesseract1.224745
tutaf (old: tutaltuttip)5Dtut alterfastegium,tut atop invertedtuttip1.274755
tutatoa sirco4Dtruncated tetrahedron atoptruncated octahedron atopsmall rhombicuboctahedron...
tutatobcu4Dtutatoe orthobicupola
tutatoe augrip4Dtutatoe-augmentedgrip
tutatoe gybcu4Dtutatoe gyrobicupola
tutatoe, tut || toe, K-4.764Dtruncated tetrahedron atoptruncated octahedron,truncated-tetrahedral cap ofprismatorhombated pentachoron, tetrahedral canticupola1.612452
tutatope5Dtut atoptope,tut-first cap ofpattix1.848423
tutcupa toe (alt.: tutaltut toetric)5Dtuta atoptoe, (tut,invtut,toe)-trigonic1.620185
tutcupip5Dtuttip atop invertedtuttip,tuta-prism, medial segment ofrittip1.322876
tutdip6Dtruncated-tetrahedron duoprism1.658312
tutepe4Dblend of 2tepes0.790569
tutic3Dblend of 2truncated cubes1.778824
tutrip3Dtwotripcupolaic blend, gyratedblend of 2digonal cupola, Phillips head0.763763
tutrippapy4Dtutrip pyramid, internalblend of 2trippies0.774597
tutrippy4Dexternalblend of 2trippies...
tuttip, K-4.574Dtruncated-tetrahedron prism1.274755
tuttipa toe (alt.: tuttut totric)5Dtuttip atoptoe, (tut,tut,toe)-trigonic1.632993
tuttipa tope5Dtuttip atoptope,tutatoe-prism,tuttip-first cap ofprippip1.688194
tutut3Dtwotutcupolaic blend, gyratedblend of 2truncated tetrahedra1.172604
twacube5Ddodecagon - cube duoprism2.117085
twaddip4Ddodecagonal-dodecagonal duoprism2.732051
twagy griddip4Dtwelve-gyro-augmentedgreat-rhombated-icosidodecahedral prism
twagy tiddip4Dtwelve-gyro-augmentedtruncated-icosidodecahedral prism
twau doaid4Ddeep mono-diminishedrotunda of ex, 12-augmenteddoe || id1.618034
twau griddip4Dtwelve-(ortho-)augmentedgreat-rhombated-icosidodecahedral prism
twau iddip4Dtwelve-augmentedicosidodecahedral-prism
twau sridati4Dtwelve-augmentedsridati
twau sriddip4Dtwelve-augmentedsriddip
twau tiddip4Dtwelve-(ortho-)augmentedtruncated-icosidodecahedral prism
twau tipe4Dtwelve-augmentedtruncated-icosahedral prism
twausniddip4Dtwelve-augmentedsniddip
twip3Ddodecagonal prism1.995508

U

...3Du q3o, variation oftriangular prism1.290994
...3Du x3o, variation oftriangular prism,vertex figure ofrectified hecatonicosachoron1.154701
...3Du x4o, variation ofcube1.224745
...3Du x5o, variation ofpentagonal prism1.312862
...3Du x6o, variation ofhexagonal prism1.414214
...3Du3o3x, variation ofcuboctahedron,Waterman polyhedron number 3 wrt. face-centered cubiclattice A3 centered at a shallow hole1.541104
...3Du3o4x, variation ofsmall rhombicuboctahedron2.040640
...3Du3x3o, variation oftruncated tetrahedron1.732051
...3Du3x4o, variation oftruncated octahedron,Waterman polyhedron number 5 wrt. face-centered cubiclattice A3 centered at a lattice point2.236068
...2Dpartially contractedhexagonal tiling
...2DuBxx3xoAo3xooA3*a&#zx
...3Dhexagonal dipyramid
...3Duo ou&#h, shorter variant ofdigonal antiprism1.118034
...4DWaterman polychoron number 3 wrt. cyclo-pentachoriclattice A4 centered at a lattice point1.732051
...3DWaterman polyhedron number 6 wrt. face-centered cubiclattice A3 centered at a lattice point
...3Ddiagonal square wedge, line atop dual square1.069045
ux10Dhendecaxennon, undecaxennon, 10Dsimplex (α10), pyrodak(id),decayottal pyramid,Gosset polytope 090.674200

V

...3Dv f3o, variation oftriangular prism,vertex figure ofrasishi0.983956
...3Dv f5/2o, variation of5/2-prism,vertex figure ofragashi0.905040
...3Dv x3o, variation oftriangular prism,vertex figure ofrectified great grand stellated hecatonicosachoron0.654847
...3Dv x5o, variation ofpentagonal prism,vertex figure ofragishi0.905040
...3Dv3o3x, variation ofcuboctahedron,vertex figure ofgadtaxady0.820211
...3Dv3o5f, variation ofsrid, hull oftiggy2.757554
...3Dv3x3o, variation oftruncated tetrahedron,vertex figure ofsidtaxhi0.975835
...3Dv3x5f, variation ofgrid, hull ofgaquatid4.323687
vee9Dpentacosidodecayotton,enneacross (β9), aeroxenn(id),enneazettal antiprism,vertex figure ofka,Gosset polytope 61,1,lattice C9 contact polytope (span of its small roots), equatorial cross-section of vertex-firstka0.707107
...3Daxially trigonal variant of pentagonal rotunda...

W

...3Dw x4o, variation ofcube1.398966
...3Dw x8o, variation ofoctagonal prism, hull of8/3-prism1.778824
...3Dw3x3o, variation oftruncated tetrahedron1.973010
...3Dw3x4x, variation ofgirco, hull ofcotco3.193704
wacbinant5Dsphenary cellibiprismatopenteractipenteractitriacontaditeron1.192297
waco, J863Dsphenocorona
...4Dexternal blend of thesphenocorona-prism and acube-pyramid,cubic-pyramid-augmentedsphenocorona-prism
wamco, J883Dsphenomegacorona
wavathi4Dsphenoverted triakishecatonicosachoron1.662508
wavaty4Dsphenoverted triakisicositetrachoron1.082392
wavaxixog6Dsphenoverted hexeracti-hexeracti-hexacontatetrapeton0.819496
wavdatixady4Dsphenoverted ditrigonary hexacosadishecatonicosachoron1.258409
wavhiddix4Dsphenoverted hecatonicosadishexacosachoron5.330704
wavhiddixa5Dsphenoverted hecatonicosadishexacosachoron alterprism5.345177
wavicoca3Dsphenoverted cubaticubatiapeiratic honeycomb
wavinant5Dsphenoverted penteractipenteractitriacontaditeron0.792893
wavitoth4Dsphenoverted tesseractitesseractihexadecachoron0.765367
wavook8Dsphenoverted octeracti-octeracti-diacosipentacontahexazetton0.870264
...2DWells' "hyperbolic" {4,5} polyhedron
...2DWells' infinite polyhedron from theike/oct diamond structure
wovsosaz7Dsphenoverted hepteracti-hepteracti-hecatonicosoctaexon0.845261
...4Dwx ox3xx4oo&#zx
...4Dwx ox3xx4xx&#zx
...4Dtricupe variant wx xx3oq&#q1.402029039

X

...3Dx f3o, variation oftriangular prism1.059565
...3Dx f5/2o, variation of5/2-prism,vertex figure ofrofix0.986715
...3Dx h3o, variation oftriangular prism1.118034
...3Dx q3o, variation oftriangular prism,vertex figure ofrectified icositetrachoron0.957427
...3Dx q4o, variation ofcube1.118034
...3Dx u3o, variation oftriangular prism1.258306
...3Dx v5o, variation ofpentagonal prism,vertex figure ofrigfix0.725530
...3Dhyperbolic xØo4x6o4o tesselation0.5i
...3Dhyperbolic xØx3o5x *c4o tesselation0.747674i
...3Dx3(-x)5f, variation ofgrid1.618034
...3Dx3/2β3x (?)...
...3Dx3f4o, variation oftruncated octahedron, hull ofsiddo, hull ofpassipsido2.176251
...3Dx3f5o, variation ofti, hull ofraded, hull ofkri3.463334
...5Dhyperbolic (order 3) triacontiditeric pentacomb, hyperbolicGosset pentacomb 21,1,10i
...4Dhyperbolic x3o3o3o *b3o3*c tesselation0.387298
...3Dhyperbolic x3o3o3x5*a tesselation1.272020i
...3Dhyperbolic x3o3o4o4*b tesselation0.462910
...4Dx3o3o4q, variation ofsidpith1.870829
...3Dhyperbolic x3o3o5o3*a tesselation0.250437i
...4Dx3o3o5v, variation ofsmall disprismatohexacosihecatonicosachoron3.835128
...4Dhyperbolichex-ex tetracomb0.171780i
...2Dhyperbolic order 3 trigonal-horocyclic tiling0.433013i
...3Dhyperbolic x3o3oPo4*b tesselation...
...4Dx3o3β4o (?)...
...4Dx3o3β4x (?)...
...4Dx3o3β5o (?)...
...4Dx3o3β5x (?)...
...3Dhyperbolic x3o3x3o5*a tesselation1.118425i
...4Dhyperbolic order 4icositetrachoral tetracomb0i
...3Dhyperbolic x3o4o3x5*a tesselation, cyclotruncated dodecahedral-octahedral honeycomb
...3Dhyperbolic x3o4o4o4*a tesselation0i
...4Dx3o4β3o (?)...
...4Dx3o4s4o (?)...
...3Dhyperbolic honeycomb x3o4x3o4x3o4*aØ*d *bØ*e *cØ*f...
...3Dhyperbolic x3o4x3o5*a tesselation0.919229i
...2Dhyperbolic dipentagonal tiling of family o3o4o5*a0.956676i
...3Dhyperbolic x3o5o6o tesselation0.465341
...3Dhyperbolic x3o5x3o5*a tesselation
...3Dhyperbolic honeycomb x3o5x3o5x3o5*aØ*d *bØ*e *cØ*f...
...3Dhyperbolic x3o5x5o3*a tesselation0.747674i
...3Dhyperbolic x3o5x *b4o tesselation0.747674i
...3Dhyperbolic x3o6o3o6*a honeycomb, hyperbolic triangular-tiling - hexagonal-tiling honeycomb0i
...3Dhyperbolic x3oØo3*a4oØo4*a tesselation, noblecuboctahedral honeycomb0i
...3Dhyperbolic x3oØo4*a3oØo4*a tesselation
...3Dhyperbolic x3o:s3s4s honeycomb...i
...3Dhyperbolic x3o:s3s5s honeycomb...i
...3Dhyperbolic x3o:s3s6s honeycomb...i
...3Dhyperbolic x3o:s3sPs honeycomb...i
...3Dx3q3o, variation oftruncated tetrahedron1.442951
...3Dx3β3o (?)...
...4Dx3β3o3o (?)...
...4Dx3β3o3β (?)...
...4Dx3β3o3x (?)...
...4Dx3β3o4o (?)...
...4Dx3β3o4β (?)...
...4Dx3β3o4x (?)...
...4Dx3β3o5o (?)...
...4Dx3β3o5β (?)...
...4Dx3β3o5x (?)...
...4Dx3β3β3x (?)...
...4Dx3β3β4o (?)...
...4Dx3β3β4β (?)...
...4Dx3β3β4x (?)...
...4Dx3β3β5o (?)...
...4Dx3β3β5β (?)...
...4Dx3β3β5x (?)...
...4Dx3β3x4β (?)...
...4Dx3β3x5β (?)...
...3Dx3β4o (?)1.581139
...4Dx3β4o3o (?)...
...4Dx3β4o3β (?)...
...4Dx3β4o3x (?)...
...4Dx3β4β3x (?)...
...3Dx3β5o (?)2.478019
...3Dx3u3o, variation oftruncated tetrahedron1.837117
...3Dx3u4o, variation oftruncated octahedron2.549510
...3Dx3v3o, variation oftruncated tetrahedron,vertex figure ofdattady0.935414
...3Dx3w3o, variation oftruncated tetrahedron2.120453
...3Dx3w4o, variation oftruncated octahedron, hull ofrah, hull ofsnu2.956796
...3Dhyperbolic x3x3o3o5*a tesselation1.072098i
...3Dhyperbolic x3x3o3x5*a tesselation1.816256i
...2Dhyperbolic shieldo-trigonal-horocyclic tiling0.829156i
...4Dx3x3β3o (?)...
...4Dx3x3β4o (?)...
...4Dx3x3β5o (?)...
...3Dx3x3u, variation oftruncated octahedron,Waterman polyhedron number 5 wrt. face-centered cubiclattice A3 centered at a shallow hole2.091650
...3Dhyperbolic x3x3x3o5*a tesselation1.601395i
...3Dhyperbolic x3x3x3x5*a tesselation2.339260i
...5Dhyperbolic x3x4o3o3o4o pentacomb1.414214i
...4Dtruncated hyperbolic order 4 icositetrachoral tetracomb1.414214i
...5Dhyperbolic x3x4o3o4o3o pentacomb0.447214i
...3Dhyperbolic x3x4o3o5*a tesselation0.869999i
...3Dhyperbolic x3x4o3x5*a tesselation
...3Dhyperbolic x4x4o *b3x tesselation, hyperbolic runcicantic o3o4o4x tesselation2.090770i
...2Dhyperbolic shieldotetrapentagonal tiling of family o3o4o5*a, ditrigonal tiling of family o3o4o5*a0.874835i
...3Dhyperbolic x3x4o6o tesselation0.447214i
...3Dx3x4q, variation ofgreat rhombicuboctahedron,Waterman polyhedron number 7 wrt. face-centered cubiclattice A3 centered at a lattice point2.645751
...4Dx3x4β3o (?)...
...3Dhyperbolic x3x4x3o5*a tesselation
...3Dhyperbolic x3x4x3x5*a tesselation
...4Dhyperbolic x3x4x3x8o tesselation1.864101i
...2Dhyperbolic omnitruncated tiling of family o3o4o5*a1.456608i
...3Dhyperbolic x3x5o3o5*a tesselation0.786151i
...3Dhyperbolic x3x5x3x5*a tesselation, hyperbolic omnitruncated dodecahedral-icosahedral honeycomb1.798907i
...3Dhyperbolic x3x:s3s4s honeycomb, hyperbolic truncatedx3o:s3s4s honeycomb...i
...3Dhyperbolic x3x:s3s5s honeycomb, hyperbolic truncatedx3o:s3s5s honeycomb...i
...3Dhyperbolic x3x:s3s6s honeycomb, hyperbolic truncatedx3o:s3s6s honeycomb...i
...3Dhyperbolic x3x:s3sPs honeycomb, hyperbolic truncatedx3o:s3sPs honeycomb...i
...4Dtesseractic tetracomb
...3Dhyperbolic x4o3o4x4*b tesselation0.5i
...3Dhyperbolic x4o3o5o3*a tesselation0.208191i
...3Dhyperbolic x4o3x3x3*b tesselation1.553774i
...3Dhyperbolic x4o4o *b3o tesselation, hyperbolic alternated o3o4o4x tesselation0.5i
x4oPo2Dfamily of (generally hyperbolic) order P square tilings
...3Dfamily of (generally hyperbolic) x4oPo4x honeycombs
...3Dhyperbolic x4s4o *b3s tesselation...
...3Dhyperbolic x4x3o8o tesselation0.594604i
...3Dhyperbolic x4x3x8o tesselation1.864101i
...3Dhyperbolic x4x4o4o4*a tesselation0.594604i
...3Dhyperbolic x4x4o5o tesselation0.720524i
...3Dhyperbolic x5/2o5o4o honeycomb, hyperbolic small stellated dodecahedral honeycomb0.437016
...3Dx5/2β5o (?)1.401259
...3Dhyperbolic x5o3o3o3*a tesselation0.573060i
...4Dhyperbolic small cellated dishecatonicosachoral honeycomb, hyperbolic cellated order 5 hecatonicosachoral honeycomb1.272020i
...3Dhyperbolic x5o3o4o3*a tesselation0.336860i
...3Dhyperbolic x5o3o5o3*a tesselation
...3Dhyperbolic x5o5o *b5/2o honeycomb0.393076i
...2Dhyperbolic quarter order 6 square tiling
...3Dhyperbolic x8o4o *b3o tesselation0.321797i
...4DxAFxx3ooxxF3Fxoxo3ooffx&#zx
xedrag6Dhexeractidiminishedrectified hexacontatetrapeton, square cuboctahedroltriate, scaliform dodecadiminishedrectified hexacontatetrapeton1
...4DxFfoo3xoxxF3fxoxo3ooffx&#zx
...4DxFfxo3xoxoF3fxooo3oofFx&#zx
...3Dxfo3foo5oxf&#zx
...3Dp60-r60, 41st stellation ofti
...3Dexpansion of41th stellation of truncated icosahedron
...3DxfoE3fooo5xuFx&#zxt
...4DFxo xfo3oox5xxx&#zxt
...4DxfofxxfoFxfxo3ooxxoFxFoxxoo3oxfxFofxxfofx&xt (F=ff=x+f)
...4Dxfooo5xofxo oxofx5ooxox&#zx, icosapentadiminishedex
...4Dtrigonalmibdi-laced wedge1
xhi4Dhexacosihecatonicosachoron, bitruncatedhecatonicosachoron, bitruncatedhexacosachoron7.579634
..., xhi || thi5D(degenerate)xhi atopthi∞   i.e. flat in euclidean space
xhidy4Dhexacosihecatonicosadishecatonicosachoron3
xhip5Dhexacosihecatonicosachoron prism, bitruncated-hecatonicosachoron prism, bitruncated-hexacosachoron prism7.596108
...3Dhyperbolic order ∞azazat honeycomb0.5
...3Dhyperbolic honeycomb x∞x5o6o0.363271i
xithi4Dhexacositriakishecatonicosachoron3.872983
...3Dxo oq&#q,tetrahedron with one shorter edge,vertex figure oftisdip0.836660
...3Dxo ox&#h, longer variant ofdigonal antiprism,vertex figure ofdeca0.935414
...3Dxo ox&#k, longer variant ofdigonal antiprism,vertex figure ofcont0.989219
...3Dxo ox&#q, longer variant ofdigonal antiprism,vertex figure oftriddip0.790569
...4Dxo3oo ox&#q, q-laced trigonalscalene0.804400
...5Dxo3oo3oo3ox&#q, longer variant ofpentachoral antiprism,vertex figure ofstaf0.866025
...4Dxo3oo3oo&#q, taller variant oftetrahedral pyramid0.784465
...4Dxo3oo3ox&#q, longer variant oftetrahedral antiprism,vertex figure ofscad0.866025
...3Dxo3oo&#q, longer variant oftrigonal pyramid,vertex figure oftepe0.774597
...4Dcyclo-hexagonally diminishedico,tegum sum of 2 bi-dual (x,q)-triddips1
...3Dxo3ox&#h, longer variant oftrigonal antiprism, cyclo-hexadiminishedco,vertex figure ofbatatoh1
...3Dxo3ox&#q, longer variant oftrigonal antiprism,vertex figure ofspid0.866025
...4Dtegum sum of 2 mutually inverted (x,u)-tips2
...3Dvertex figure ofsmall prismated icositetrachoron0.541196
...4Dtetra-augmented axially-octahedral ursachoron xoBo3ofox3xooo&#xt...
...4Dxofo3ofox5xoxx&#xt3.077684
...4Dtetra-augmented axially-tetrahedral ursachoron xofo3ooox3oxoo&#xt...
...3Dpentagonal rhombic barrel
...4Dtriaugmented trigonalmibdi-laced wedge...
...4DxofxxFfooFxfo3xxxoFxxxFoxxx3ofxFoofFxxfox&#xt
xog6Dhexeractihexacontatetrapeton, tritruncated hexeract, tritruncated hexacross2.549510
...4Dxoofoox3ofxoxfo5xoxxxox&#xt
...4DxooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#xt
...4DxooFxxFfooFxofo3xxFooFxxxFoxFxx3ofooFoofFxxfoox&#xt
...4DxoofxxFfooFxofo3xxFxoFxxxFoxFxx3ofoxFoofFxxfoox&#xt
...4D:xoqo:4:xxox:3:oooo:4:oxxx:&##x
xorene8Dexirhombated enneazetton1.732051
...4Dhexastraticike-first cap ofrectified hexacosachoron3.077684
...4DxoxFoFxox3oxoooooxo5ooxofoxoo&#xt
...4DxoxFxFxox3oxfoxofxo5xxoxxxoxx&#xt
...4Dike atopid atopsrid atopti
...4DxoxxFxxox3oxoxoxoxo5ooxoooxoo&#xt
...2Dfamily of (generally hyperbolic) P-gonal tilings of order P
...3DWaterman polyhedron number 4 wrt. body-centered cubiclattice C3* centered at a hole
...4Ddecachoron-derived Gévay polychoron,Waterman polychoron number 4 wrt. cyclo-pentachoriclattice A4 centered at a lattice point2
...4DPowertope {p}{8}sqrt[1+1/sqrt(2)]/sin(π/p)
...3Dq-laced digonal cupola,vertex figure ofsrip0.906327
...4DxxfoF3oxxFx3xFxxo3Fofxx&#zx
...4Dmagnaursachoron, cell-expanded tetrahedralursachoron...
xxo ooo3oxx&#xt4Dline ||trip || {3}, stack oftepe andtriddip
...3Dvertex figure ofcope0.894427
...4DxxxFooAFxxAxxFx3oxFxxAxxxFooFxx3xfoxFoofFxxFoox&#xt
...4DxxxoooFFFAAA 2 FxfoFfxFofxo 2 xfFFfoFoxxof 2 fFxfoFoxFofx &#zx
...4DxxxoooFFFAAABxxxF FxfoFfxFofxooVoof xfFFfoFoxxofooVof FAoFxAxoAxFoxxxBF&#zx
...4DxxxoooFFFAAAxxF FxfoFfxFofxoVof xfFFfoFoxxofoVf FAoFxAxoAxFoxxF&#zx

Y

yab8Dmyriaheptachiliadiacosioctaconta-diacositetraconta-zetton1

Z

zahesa8Dzee ||hesa1
zarez8Dzee atoprez,rectified diacosipentacontahexazetton half1
zee (old: hio)7Dhecatonicosoctaexon,heptacross (β7), aerozett(id),heptapetal antiprism,vertex figure ofek,Gosset polytope 41,1,lattice C7 contact polytope (span of its small roots), equatorial cross-section of vertex-firstek0.707107
zeep8Dhecatonicosoctaexon prism,vertex figure ofriv0.866025
zeepy8Dzee pyramid,heptacross pyramid, vertex pyramid ofek0.707107
zucypit5Dschmoozed cyclopentachoric tetracomb, schmoozed pentachoric-dispentachoric tetracomb

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