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Lace towers are defined to be stacks of lace prisms, therefore bistratic lace towers are polytopes withexactly 3 vertex layers aligned atop of each other, which all share a commonCoxeter symmetry.It shall be pointed out that lace prisms generally allow to considerdifferent edge length symbols. But in this page we restrict to bistraticCRF lace towers, i.e. which have unit edges only and furthermore their 2D faces are considered to be regular. Therefore non-unit edges only can occur as false ones within the medial layer, connecting2 coplanar lacing faces of the respective segments.
2D
3D
4D
For comparision purposes in the following listings those will be oriented such that the top circumradius is smaller or at most equal to the bottom one.Furthermore, when equal, that the height(1,2) is smaller or equal to the height(2,3).Also, whenever the across symmetry or a reducible part of it has an additional symmetry of itsDynkin symbol,then it will be oriented within lower lexicographic order, except that mereStott expansion are aligned,i.e. thatooo andxxx are given the same spott, in fact the lexicographical place of the latter one. The same also is used generally foroAo andxBx, whenA is any specific edge or pseudo edge length andB = A+x. (For more clarity on the according groupings the first column in each table is added to provide a visually attractingcorresponding logical paranthesis.)
In the following lists onlyaxial (external)blends are explicitly mentioned in the remarks columns,as these thus happen to be "mere" axial stacks. None the less, those casually may happen to be special when some of the lacing facets becomecollinaer / coplanar / corealmic / ... and thus can be considered to be blended in turn. In case this then could be seen in the equatorial dihedral angles column.
---- 2D (up)----
Here we have just 3 cases:
| Stott Type | Lace Tower | Polygon | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oqo&#xt | {4} | both heights = 1/sqrt(2) = 0.707107 q = sqrt(2) = 1.414214 | 90° | |
ofx&#xt | {5} | height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785 height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057 f = (1+sqrt(5))/2 = 1.618034 | 108° | |
xux&#xt | {6} | both heights = sqrt(3)/2 = 0.866025 u = 2 | 120° |
---- 3D (up)----
Here the enumeration is obvious. We just have to select the bistraticJohnson solids with trigonal axial symmetry.
| Stott Type | Lace Tower | Polyhedron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oox3oxo&#xt | trig. gyroelong. pyr. | blend oftet andoct | at {3}-{3} = 180° resulting in lacing rhombs (thus non-CRF) | |
oox3xux&#xt | tut | (acrossu) = 180° resulting in lacing {6} | ||
oxo3ooo&#xt | tridpy (J12) | blend of 2tets | at {3}-{3} = arccos(-7/9) = 141.057559° | |
oxo3xxx&#xt | tobcu (J27) | blend of 2tricues | at {3}-{3} = arccos(-7/9) = 141.057559° at {4}-{4} = arccos(-1/3) = 109.471221° | |
oxx3xxo&#xt | co | blend of 2 gyratedtricues | at {3}-{4} = arccos[-1/sqrt(3)] = 125.264390° | |
oxx3ooo&#xt | etripy (J7) | blend oftet andtrip | at {3}-{4} = arccos[-sqrt(8)/3] = 160.528779° | |
oxx3xxx&#xt | etcu (J18) | blend oftricu andhip | at {3}-{4} = arccos[-sqrt(8)/3] = 160.528779° at {4}-{4} = arccos[-sqrt(2/3)] = 144.735610° | |
ofx3xoo&#xt | teddi (J63) | (acrossf) = 180° resulting in lacing {5} | ||
oAo3xox&#xt | tautip (J51) | A = (1+sqrt(6))/2 = 1.724745 | - | |
xBx3xox&#xt | tauhip (J57) | B = (3+sqrt(6))/2 = 2.724745 | - | |
oxo6sox&#xt | gyetcu (J22) | blend oftricu andhap | at {3}-{3} ≈ 169.428208° at {3}-{4} ≈ 153.635039° |
Here the enumeration is obvious. We just have to select the bistraticJohnson solids with tetragonal axial symmetry.
| Stott Type | Lace Tower | Polyhedron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oox4oxo&#xt | gyesp (J10) | blend ofsquippy andsquap | at {3}-{3} ≈ 158.571770° | |
oxo4ooo&#xt | oct | blend of 2squippies | at {3}-{3} = arccos(-1/3) = 109.471221° | |
oxo4xxx&#xt | squobcu (J28) | blend of 2squacues | at {3}-{3} = arccos(-1/3) = 109.471221° at {4}-{4} = 90° | |
oxx4xxo&#xt | squigybcu (J29) | blend of 2 gyratedsquacues | at {3}-{4} = arccos(-sqrt[(3-2 sqrt(2))/6]) = 99.735610° | |
oxx4ooo&#xt | esquipy (J8) | blend ofsquippy andcube | at {3}-{4} = arccos[-sqrt(2/3)] = 144.735610° | |
oxx4xxx&#xt | escu (J19) | blend ofsquacu andop | at {3}-{4} = arccos[-sqrt(2/3)] = 144.735610° at {4}-{4} = 135° | |
oqo4xox&#xt | co | at {3}-{4} = arccos[-1/sqrt(3)] = 125.264390° | ||
oxo8sox&#xt | gyescu (J23) | blend ofsquacu andoap | at {3}-{3} ≈ 151.330128° at {3}-{4} ≈ 141.594518° |
Here the enumeration is obvious. We just have to select the bistraticJohnson solids with pentagonal axial symmetry.
| Stott Type | Lace Tower | Polyhedron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oox5oxo&#xt | gyepip (J11) | blend ofpeppy andpap | at {3}-{3} = arccos(-sqrt(5)/3) = 138.189685° | |
oxo5ooo&#xt | pedpy (J13) | blend of 2peppies | at {3}-{3} = arccos[(4 sqrt(5)-5)/15] = 74.754736° | |
oxo5xxx&#xt | pobcu (J30) | blend of 2pecues | at {3}-{3} = arccos[(4 sqrt(5)-5)/15] = 74.754736° at {4}-{4} = arccos(1/sqrt(5)) = 63.434949° | |
oxx5xxo&#xt | pegybcu (J31) | blend of 2 gyratedpecues | at {3}-{4} = arccos(sqrt[(3-sqrt(5))/6]) = 69.094843° | |
oxx5ooo&#xt | epeppy (J9) | blend ofpeppy andpip | at {3}-{4} = arccos(-sqrt[(10-2 sqrt(5))/15]) = 127.377368° | |
oxx5xxx&#xt | epcu (J20) | blend ofpecu anddip | at {3}-{4} = arccos(-sqrt[(10-2 sqrt(5))/15]) = 127.377368° at {4}-{4} = arccos(-sqrt[(5-sqrt(5))/10]) = 121.717474° | |
ofx5xox&#xt | pero (J6) | (acrossf) = 180° resulting in lacing {5} | ||
oxo10sox&#xt | gyepcu (J24) | blend ofpecu anddap | at {3}-{3} ≈ 132.624012° at {3}-{4} ≈ 126.964118° |
Here the enumeration is obvious. We just have to select the bistraticJohnson solids with rectangular axial symmetry.And the prisms of the subdimensional case, for sure.
| Stott Type | Lace Tower | Polyhedron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oox oyo&#xt | tridpy (J12) | y = sqrt(8/3) = 1.632993 | - | |
oox xYx&#xt | etidpy (J14) | Y = sqrt[(11+4 sqrt(6))/3] = 2.632993 | - | |
oxo oxo&#xt | oct | blend of 2squippies | at {3}-{3} = arccos(-1/3) = 109.471221° | |
oxo oxx&#xt | autip (J49) | blend ofsquippy andtrip | at {3}-{3} = arccos[-sqrt(2/3)] = 144.735610° at {3}-{4} = arccos[-(sqrt(6)-1)/sqrt(12)] = 114.735610° | |
oxx xxo&#xt | gybef (J26) | blend of 2 gyratedtrips | at {3}-{4} = 150° | |
oqo xxx&#xt | cube | at {4}-{4} = 90° | ||
ofx xxx&#xt | pip | at {4}-{4} = 108° | ||
oAx xox&#xt | bautip (J50) | A = (1+sqrt(6))/2 = 1.724745 | - | |
xox oqo&#xt | oct | - | ||
xox xwx&#xt | esquidpy (J15) | - | ||
xux xxx&#xt | hip | at {4}-{4} = 120° | ||
o(qo)o o(oq)o&#xt | oct | blend of 2squippies | at {3}-{3} = arccos(-1/3) = 109.471221° | |
o(qo)o x(xw)x&#xt | esquidpy (J15) | at {3}-{3} = arccos(-1/3) = 109.471221° at {4}-{4} = 90° | ||
x(wx)x x(xw)x&#xt | squobcu (J28) | blend of 2 gyratedsquacues | at {3}-{3} = arccos(-1/3) = 109.471221° at {4}-{4} = 90° | |
(xu)o(xu) (ho)B(ho)&#xt | pabauhip (J55) | B = sqrt(3)+sqrt(2) = 3.146264 | - |
---- 4D (up)----
| Stott Type | Lace Tower | Polychoron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oox3oxo3ooo&#xt | aurap | blend ofoctpy andrap | attet-{3}-tet = arccos[-(1+3 sqrt(5))/8] = 164.477512° attet-{3}-oct = arccos[-(3 sqrt(5)-1)/8] = 135.522488° | |
oox3oxo3xxx&#xt | arse aurap | blend oftetatut andcoatut | attricu-{6}-tricu = arccos[-(1+3 sqrt(5))/8] = 164.477512° atoct-{3}-tet = arccos[-(3 sqrt(5)-1)/8] = 135.522488° | |
oox3xxo3oxx&#xt | srip | blend ofoctatut andcoatut | attricu-{6}-tricu = 180° resulting in lacingco attrip-{3}-oct = arccos[-sqrt(3/8)] = 127.761244° | |
oox3xfo3oox&#xt | octu | (acrosso3f .) = 180° resulting in lacingteddi (across. f3o) = 180° resulting in lacingteddi | ||
oox3xux3oox&#xt | octum | (acrosso3u .) = 180° resulting in lacingtut (across. u3o) = 180° resulting in lacingtut | ||
oox3xux3xoo&#xt | deca | (acrosso3u .) = 180° resulting in lacingtut (across. u3o) = 180° resulting in lacingtut | ||
oxo3xox3oxo&#xt | ico | blend of 2octacoes | atsquippy-{4}-squippy = 180° resulting in lacingoct atoct-{3}-oct = 120° | |
oxo3oox3xxo&#xt | tetacoaoct | blend oftetaco andoctaco | atsquippy-{4}-trip = arccos[-sqrt(5/6)] = 155.905157° atoct-{3}-tet = arccos[-(3 sqrt(5)-1)/8] = 135.522488° atoct-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756° | |
oxo3ooo3ooo&#xt | tete | blend of 2pens | attet-{3}-tet = arccos(-7/8) = 151.044976° | |
oxo3ooo3xxx&#xt | gyspid | blend of 2tetacoes | attet-{3}-tet = arccos(-7/8) = 151.044976° attrip-{4}-trip = arccos(-2/3) = 131.810315° attrip-{3}-trip = arccos(-1/4) = 104.477512° | |
oxo3xxx3ooo&#xt | octatutbicu | blend of 2octatuts | attricu-{6}-tricu = arccos(-7/8) = 151.044976° attrip-{3}-trip = arccos(-1/4) = 104.477512° | |
oxo3xxx3xxx&#xt | tutatobcu | blend oftutatoes | attricu-{6}-tricu = arccos(-7/8) = 151.044976° attrip-{4}-trip = arccos(-2/3) = 131.810315° athip-{6}-hip = arccos(-1/4) = 104.477512° | |
oxx3oox3xxo&#xt | tetaco altut | blend oftetaco and gyratedcoatut | attrip-{4}-trip = 180° resulting in lacinggybef atoct-{3}-trip = arccos(-sqrt[27/32]) = 156.716268° attet-{3}-tricu = arccos(-7/8) = 151.044976° | |
oxx3xoo3oxx&#xt | eoctaco | blend ofoctaco andcope | atcube-{4}-squippy = 180° resulting in lacingesquipy atoct-{3}-trip = 150° | |
oxx3ooo3xxo&#xt | spid | blend of 2 gyratedtetacoes | attrip-{4}-trip = arccos(-2/3) = 131.810315° attet-{3}-trip = arccos(-sqrt(3/8)) = 127.761244° | |
oxx3xxx3xxo&#xt | tutato gybcu | blend of 2 gyratedtutatoes | attrip-{4}-trip = arccos(-2/3) = 131.810315° athip-{6}-tricu = arccos(-sqrt(3/8)) = 127.761244° | |
oxx3ooo3ooo&#xt | etepy | blend ofpen andtepe | attet-{3}-trip = arccos[-sqrt(15)/4] = 165.522488° | |
oxx3ooo3xxx&#xt | etetaco | blend oftetaco andcope | attet-{3}-trip = arccos[-sqrt(15)/4] = 165.522488° atcube-{4}-trip = arccos[-sqrt(5/6)] = 155.905157° attrip-{3}-trip = arccos[-sqrt(5/8)] = 142.238756° | |
oxx3xxx3ooo&#xt | eoctatut | blend ofoctatut andtuttip | athip-{6}-tricu = arccos[-sqrt(15)/4] = 165.522488° attrip-{3}-trip = arccos[-sqrt(5/8)] = 142.238756° | |
oxx3xxx3xxx&#xt | etutatoe | blend oftutatoe andtope | athip-{6}-tricu = arccos[-sqrt(15)/4] = 165.522488° atcube-{4}-trip = arccos[-sqrt(5/6)] = 155.905157° athip-{6}-hip = arccos[-sqrt(5/8)] = 142.238756° | |
xxo3oxx3ooo&#xt | tetatutaoct | blend oftetatut andoctatut | attricu-{6}-tricu = arccos[-(3 sqrt(5)-1)/8] = 135.522488° attet-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756° | |
xxo3oxx3xxx&#xt | coatoatut | blend ofcoatoe andtutatoe | attricu-{6}-tricu = arccos[-(3 sqrt(5)-1)/8] = 135.522488° athip-{6}-tricu = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756° atcube-{4}-trip = arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157° | |
ooo3oxo3ooo&#xt | hex | blend of 2octpies | attet-{3}-tet = 120° | |
ooo3oxo3xxx&#xt | tetatut bicu | blend of 2tetatuts | attet-{3}-tet = 120° attricu-{6}-tricu = 120° | |
xxx3oxo3xxx&#xt | coatobcu | blend of 2coatoes | attricu-{6}-tricu = 120° atcube-{4}-cube = 90° | |
ooo3oxx3ooo&#xt | eoctpy | blend ofoctpy andope | attet-{3}-trip = 150° | |
ooo3oxx3xxx&#xt | etetatut | blend oftetatut andtuttip | attet-{3}-trip = 150° attricu-{6}-hip = 150° | |
xxx3oxx3xxx&#xt | ecoatoe | blend ofcoatoe andtope | athip-{6}-tricu = 150° atcube-{4}-cube = 135° | |
xfo3oox3ooo&#xt | tetu | (acrossf3o .) = 180° resulting in lacingteddi | ||
xfo3oox3xxx&#xt | coatutu | (acrossf3o .) = 180° resulting in lacingteddi (acrossf . x) = 180° resulting in lacingpip attet-{3}-tricu = arccos[-sqrt(3/32) (sqrt(5)-1)] = 112.238756° | ||
oao3xox3ooo&#xt | tau ope | a = (2+sqrt(10))/3 = 1.720759 | - | |
oao3xox3xxx&#xt | tehipau tuttip | a = (2+sqrt(10))/3 = 1.720759 | attricu-{3}-tricu = arccos(1/4) = 75.522488° | |
xbx3xox3ooo&#xt | tetripau tuttip | b = (5+sqrt(10))/3 = 2.720759 | - | |
xbx3xox3xxx&#xt | tautope | b = (5+sqrt(10))/3 = 2.720759 | attricu-{3}-tricu = arccos(1/4) = 75.522488° | |
xux3oox3ooo&#xt | tip | (acrossu3o .) = 180° resulting in lacingtut | ||
xux3oox3xxx&#xt | coatotum | (acrossu3o .) = 180° resulting in lacingtut (acrossu . x) = 180° resulting in lacinghip attet-{3}-tricu = arccos[-sqrt(3/8)] = 127.761244° | ||
xx(qo)3oo(oo)3ox(oq)&#xt | tetacoa cube | blend oftetaco andcubaco | (acrossx3o .) = arccos[-(3-sqrt(8)+sqrt[30 sqrt(8)-45])/sqrt(48)] = 159.382864° (acrossx . x) = arccos[-(1-sqrt(2)+sqrt[20 sqrt(2)-15])/sqrt(12 sqrt(2))] = 141.646907° (across. o3x) = arccos[-(3-sqrt(8)+sqrt[90 sqrt(8)-135])/sqrt(128)] = 169.000195° | |
xx(qo)3xx(xx)3ox(oq)&#xt | tutatoa sirco | blend oftutatoe andsircoatoe | (acrossx3x .) = arccos[-(3-sqrt(8)+sqrt[30 sqrt(8)-45])/sqrt(48)] = 159.382864° (acrossx . x) = arccos[-(1-sqrt(2)+sqrt[20 sqrt(2)-15])/sqrt(12 sqrt(2))] = 141.646907° (across. x3x) = arccos[-(3-sqrt(8)+sqrt[90 sqrt(8)-135])/sqrt(128)] = 169.000195° | |
| ... | ||||
| Stott Type | Lace Tower | Polychoron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oox3ooo4oxo&#xt | ptacubaoct | blend ofcubpy andoctacube | atsquippy-{4}-squippy = arccos[-(sqrt(2)-1+sqrt[2 sqrt(2)-1])/2] = 152.031248° | |
oox3xxx4oxo&#xt | coaticatoe | blend ofcoatic andtoatic | atsquacu-{8}-squacu = arccos[-(sqrt(2)-1+sqrt[2 sqrt(2)-1])/2] = 152.031248° attricu-{3}-trip = arccos[(3 sqrt(6)-2 sqrt(3)-sqrt[12 sqrt(2)-6])/8] = 85.898535° | |
oox3ooo4oxx&#xt | biscpoxic | blend ofcubpy andcubasirco | atcube-{4}-squippy = 180° resulting in lacingesquipy | |
oox3xxx4oxx&#xt | biscsrico | blend ofoctatic andticagirco | atop-{8}-squacu = 180° resulting in lacingescu attricu-{3}-trip = 150° | |
oxo3oox4xxo&#xt | cubasircoaco | blend ofcubasirco andcoasirco | atsquippy-{4}-trip = arccos[-(1-sqrt(2)+sqrt[4 sqrt(2)-2])/sqrt(6)] = 127.704362° atoct-{3}-tet = arccos[-(2-3 sqrt(2)+3 sqrt[4 sqrt(2)-2])/8] = 115.898535° atcube-{4}-squap = arccos[-(sqrt[2 sqrt(2)-1]-1)/sqrt(sqrt(32))] = 98.515624° | |
oxo3ooo4ooo&#xt | hex | blend of 2octpies | attet-{3}-tet = 120° | |
oxo3ooo4xxx&#xt | pacsid pith | blend of 2cubasircoes | attet-{3}-tet = 120° attrip-{4}-trip = arccos(-1/3) = 109.471221° atcube-{4}-cube = 90° | |
oxo3xxx4ooo&#xt | coatobcu | blend of 2coatoes | attricu-{6}-tricu = 120° atcube-{4}-cube = 90° | |
oxo3xxx4xxx&#xt | tica gircobcu | blend of 2ticagircoes | attricu-{6}-tricu = 120° attrip-{4}-trip = arccos(-1/3) = 109.471221° atop-{8}-op = 90° | |
oxo3oox4xxx&#xt | cubasircoatic | blend ofcubasirco andsircoatic | attet-{3}-oct = 180° resulting in lacing trig. gyroelongated pyramids (thence non-CRF) attrip-{4}-trip = 180° resulting in lacing rhomb-prisms (thence non-CRF) atcube-{4}-squacu = 135° | |
oxx3oox4xxo&#xt | cubasircoatoe | blend ofcubasirco andsircoatoe | attrip-{4}-trip = arccos[-(2-sqrt(2)+sqrt[8 sqrt(2)-6])/3] = 164.503097° attet-{3}-tricu = arccos[-(2 sqrt(2)-3+3 sqrt[4 sqrt(2)-3])/sqrt(32)] = 146.522293° atcube-{4}-squap = arccos[-(sqrt(2)-1+sqrt[4 sqrt(2)-3])/sqrt(sqrt(32))] = 149.258250° | |
oxx3xxo4oox&#xt | coatoa sirco | blend ofcoatoe andsircoatoe | attricu-{6}-tricu = arccos[-(3-2 sqrt(2)+3 sqrt[4 sqrt(2)-3])/sqrt(32)] = 153.477707° atcube-{4}-squap = arccos[-(1-sqrt(2)+sqrt[4 sqrt(2)-3])/sqrt(sqrt(32))] = 120.741750° | |
oxx3ooo4ooo&#xt | eoctpy | blend ofoctpy andope | attet-{3}-trip = 150° | |
oxx3ooo4xxx&#xt | ecuba sirco | blend ofcubasirco andsircope | attet-{3}-trip = 150° atcube-{4}-trip = arccos[-sqrt(2/3)] = 144.735610° atcube-{4}-cube = 135° | |
oxx3xxx4ooo&#xt | ecoatoe | blend ofcoatoe andtope | athip-{6}-tricu = 150° atcube-{4}-cube = 135° | |
oxx3xxx4xxx&#xt | etica girco | blend ofticagirco andgircope | athip-{6}-tricu = 150° atcube-{4}-trip = arccos[-sqrt(2/3)] = 144.735610° atop-{8}-op = 135° | |
xoo3oxo4oox&#xt | octacoacube | blend ofoctaco andcubaco | atsquap-{4}-squippy = arccos[-sqrt(8-3 sqrt(2))/2] = 165.741750° atoct-{3}-tet = arccos[-(3-sqrt(8)+3 sqrt[4 sqrt(2)-3])/(4 sqrt(2))] = 153.477707° | |
xoo3oxx4ooo&#xt | eoctaco | blend ofoctaco andcope | atcube-{4}-squippy = 180° resulting in lacingesquipy atoct-{3}-trip = 150° | |
xoo3oxx4xxx&#xt | esircoatic | blend ofsircoatic andticcup | atop-{8}-squacu = 180° resulting in lacingescu atoct-{3}-trip = 150° | |
xox3oxo4ooo&#xt | ico | blend of 2octacoes | atsquippy-{4}-squippy = 180° resulting in lacingoct atoct-{3}-oct = 120° | |
xox3oxo4xxx&#xt | pacsrit | blend of 2sircoatics | atsquacu-{8}-squacu = 180° resulting in lacingsquobcu atoct-{3}-oct = 120° | |
xxo3oox4oxo&#xt | octasircoaco | blend ofoctasirco andcoasirco | atsquippy-{4}-trip = arccos[-(2-2 sqrt(2)+sqrt[4 sqrt(2)-2])/sqrt(12)] = 108.233141° atsquap-{4}-squippy = arccos[-(sqrt[2 sqrt(2)-1]-1)/sqrt(sqrt(32))] = 98.515624° atoct-{3}-trip = arccos[sqrt(3) (3 sqrt(2)-2-sqrt[4 sqrt(2)-2])/8] = 85.898535° | |
xxo3oox4oxx&#xt | octasircoatic | blend ofoctasirco andsircoatic | attrip-{4}-trip = arccos[-sqrt(8)/3] = 160.528779° atoct-{3}-trip = 150° atsquacu-{4}-squippy = 135° | |
xxo3ooo4oxx&#xt | octasircoacube | blend ofoctasirco andcubasirco | atcube-{4}-squippy = 90° attet-{3}-trip = 90° attrip-{4}-trip = 90° | |
xxo3xxx4oxx&#xt | toagircoatic | blend oftoagirco andticagirco | athip-{6}-tricu = 90° atop-{8}-squacu = 90° attrip-{4}-trip = 90° | |
ooo3oox4oxo&#xt | ptacubaco | blend ofcubpy andcubaco | atsquap-{4}-squippy = arccos[-(sqrt(2)-1+sqrt[4 sqrt(2)-3])/(2 sqrt[sqrt(2)])] = 149.258250° | |
xxx3oox4oxo&#xt | octasircoatoe | blend ofoctasirco andsircoatoe | attricu-{3}-trip = arccos[-(2 sqrt(6)-sqrt(3)+sqrt[12 sqrt(2)-9])/(4 sqrt[sqrt(8)])] = 152.928678° atsquap-{4}-squippy = arccos[-(sqrt(2)-1+sqrt[4 sqrt(2)-3])/(2 sqrt[sqrt(2)])] = 149.258250° attrip-{4}-trip = arccos[-(2 sqrt(2)-2+sqrt[4 sqrt(2)-3])/3] = 145.031877° | |
ooo3xox4oqo&#xt | rit | (across. o4q) = 180° resulting in lacingco | ||
xxx3xox4oqo&#xt | pabdirico | attricu-{3}-tricu = 120° (acrossx . q) = 180° resulting in lacingcube (across. o4q) = 180° resulting in lacingco | ||
ooo3ooo4oxo&#xt | cute | blend of 2cubpies | atsquippy-{4}-squippy = 90° | |
ooo3xxx4oxo&#xt | coaticbicu | blend of 2coatics | atsquacu-{8}-squacu = 90° attrip-{3}-trip = 60° | |
xxx3ooo4oxo&#xt | octa sircobcu | blend of 2octasircoes | atsquippy-{4}-squippy = 90° attrip-{4}-trip = arccos(1/3) = 70.528779° attrip-{3}-trip = 60° | |
xxx3xxx4oxo&#xt | toagircobcu | blend of 2toagircoes | atsquacu-{8}-squacu = 90° attrip-{4}-trip = arccos(1/3) = 70.528779° athip-{6}-hip = 60° | |
ooo3ooo4oxx&#xt | ecubpy | blend ofcubpy andtes | atcube-{4}-squippy = 135° | |
ooo3xxx4oxx&#xt | ecoatic | blend ofcoatic andticcup | atop-{8}-squacu = 135° attrip-{3}-trip = 120° | |
xxx3ooo3oxx&#xt | eocta sirco | blend ofoctasirco andsircope | atcube-{4}-squippy = 135° atcube-{4}-trip = arccos[-1/sqrt(3)] = 125.264390° attrip-{3}-trip = 120° | |
xxx3xxx4oxx&#xt | etoa girco | blend oftoagirco andgircope | atop-{8}-squacu = 135° atcube-{4}-trip = arccos[-1/sqrt(3)] = 125.264390° athip-{6}-hip = 120° | |
xfo3oox4ooo&#xt | octu | (acrosso3f .) = 180° resulting in lacingteddi | ||
xfo3oox4xxx&#xt | sirco aticu | (acrossf3o .) = 180° resulting in lacingteddi (acrossf . x) = 180° resulting in lacingpip | ||
xux3oox4ooo&#xt | octum | (acrossu3o .) = 180° resulting in lacingtut | ||
xux3oox4xxx&#xt | sircoa gircotum | (acrossu3o .) = 180° resulting in lacingtut (acrossu . x) = 180° resulting in lacinghip atcube-{4}-squacu = 135° | ||
oqo3ooo4xox&#xt | pabdico | - | ||
oqo3xxx4xox&#xt | dapabdi spic | atsquacu-{4}-squacu = 90° | ||
xwx3ooo4xox&#xt | dapabdi poxic | - | ||
xwx3xxx4xox&#xt | hagy gircope | atsquacu-{4}-squacu = 90° | ||
oao3xox4ooo&#xt | haucope | a = 1+1/sqrt(2) = 1.707107 | - | |
oao3xox4xxx&#xt | hau ticcup | a = 1+1/sqrt(2) = 1.707107 | atsquacu-{4}-squacu = 90° | |
xbx3xox4ooo&#xt | hautope | b = 2+1/sqrt(2) = 2.707107 | - | |
xbx3xox4xxx&#xt | hau gircope | b = 2+1/sqrt(2) = 2.707107 | atsquacu-{4}-squacu = 90° | |
oos3oos4oxo&#xt | pta cubaike | blend ofcubpy andcubaike | atsquippy-{4}-trip = arccos[-sqrt(5/6)] = 155.905157° | |
oso3oso4oox&#xt | ptaika cube | blend ofikepy andcubaike | attet-{3}-tet = 120° atsquippy-{3}-tet = arccos(-1/4) = 104.477512° | |
| ... | ||||
| Stott Type | Lace Tower | Polychoron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oxo3ooo5oox&#xt | biscex | blend ofikepy andikadoe | attet-{3}-tet = arccos[-(1+3 sqrt(5))/8] = 164.477512° | |
oxo3xxx5oox&#xt | idatiatid | blend ofidati andtiatid | attricu-{6}-tricu = arccos[-(1+3 sqrt(5))/8] = 164.477512° atpecu-{5}-pip = 126° | |
oxo3oox5xxo&#xt | doasridaid | blend ofdoasrid andidasrid | atsquippy-{4}-trip = arccos(1/sqrt(6)) = 65.905157° atoct-{3}-tet = 60° atpap-{5}-pip = 54° | |
oxo3xox5oxo&#xt | idasrid bicu | blend of 2idasrids | atsquippy-{4}-squippy = 90° atoct-{3}-oct = arccos(1/4) = 75.522488° atpap-{5}-pap = 72° | |
oxo3ooo5ooo&#xt | ite | blend of 2ikepies | attet-{3}-tet = arccos[(3 sqrt(5)-1)/8] = 44.477512° | |
oxo3ooo5xxx&#xt | doasrid bicu | blend of 2doasrids | attet-{3}-tet = arccos[(3 sqrt(5)-1)/8] = 44.477512° attrip-{4}-trip = arccos(sqrt(5)/3) = 41.810315° atpip-{5}-pip = 36° | |
oxo3xxx5ooo&#xt | idatibcu | blend of 2idatis | attricu-{6}-tricu = arccos[(3 sqrt(5)-1)/8] = 44.477512° atpip-{5}-pip = 36° | |
oxo3xxx5xxx&#xt | tidagrid bicu | blend of 2tidagrids | attricu-{6}-tricu = arccos[(3 sqrt(5)-1)/8] = 44.477512° attrip-{4}-trip = arccos(sqrt(5)/3) = 41.810315° atdip-{10}-dip = 36° | |
oxx3xoo5oxx&#xt | eidasrid | blend ofidasrid andsriddip | atcube-{4}-squippy = 135° atoct-{3}-trip = arccos[-sqrt(3/8)] = 127.761244° atpap-{5}-pip = 126° | |
oxx3xox5oxo&#xt | idasridati | blend ofidasrid andsridati | atsquippy-{4}-trip = arccos[-sqrt(5/6)] = 155.905157° atpap-{5}-pap = 144° atoct-{3}-tricu = arccos[-(3 sqrt(5)-1)/8] = 135.522488° | |
oxx3xxo5oox&#xt | idatiasrid | blend ofidati andsridati | attricu-{6}-tricu = arccos(-1/4) = 104.477512° atpap-{5}-pip = 90° | |
oxx3ooo5ooo&#xt | eikepy | blend ofikepy andipe | attet-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756° | |
oxx3ooo5xxx&#xt | edoasrid | blend ofdoasrid andsriddip | attet-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756° atcube-{4}-trip = arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157° atpip-{5}-pip = 108° | |
oxx3xxx5ooo&#xt | eidati | blend ofidati andtipe | athip-{6}-tricu = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756° atpip-{5}-pip = 108° | |
oxx3xxx5xxx&#xt | etidagrid | blend oftidagrid andgriddip | athip-{6}-tricu = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756° atcube-{4}-trip = arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157° atdip-{10}-dip = 108° | |
xoo3oox5oxo&#xt | ikadoaid | blend ofikadoe anddoaid | atpap-{5}-peppy = 180° resulting in lacinggyepip | |
xoo3oxo5oox&#xt | ikaidadoe | blend ofikaid anddoaid | atpap-{5}-peppy = 108° atoct-{3}-tet = arccos(-1/4) = 104.477512° | |
xoo3oxx5ooo&#xt | eikaid | blend ofikaid andiddip | atpip-{5}-peppy = 126° atoct-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756° | |
xoo3oxx5xxx&#xt | esridatid | blend ofsridatid andtiddip | atdip-{10}-pecu = 126° atoct-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756° | |
xoo3ooo5oxx&#xt | eikadoe | blend ofikadoe anddope | atpip-{5}-peppy = 162° | |
xoo3xxx5oxx&#xt | etiatid | blend oftiatid andtiddip | atdip-{10}-pecu = 162° attricu-{3}-trip = arccos[-sqrt(3/8)] = 127.761244° | |
xoo3ofx5xox&#xt | tiduro | (acrosso3f .) = 180° resulting in lacingteddi (across. f5o) = 180° resulting in lacingpero | ||
xox3oxo5oox&#xt | biscrox | blend ofikaid andidasrid | atpap-{5}-peppy = 180° resulting in lacinggyepip atoct-{3}-oct = arccos[-(1+3 sqrt(5))/8] = 164.477512° | |
xox3oxo5ooo&#xt | rite | blend of 2ikaids | atpeppy-{5}-peppy = 72° atoct-{3}-oct = arccos[(3 sqrt(5)-1)/8] = 44.477512° | |
xox3oxo5xxx&#xt | sridatidbicu | blend of 2sridatids | atpecu-{10}-pecu = 72° atoct-{3}-oct = arccos[(3 sqrt(5)-1)/8] = 44.477512° | |
xox3oxx5xxo&#xt | srida tidati | blend ofsridatid andtiatid | atpecu-{10}-pecu = 108° atoct-{3}-tricu = 60° | |
xox3ooo5oxo&#xt | ikadobcu | blend of 2ikadoes | atpeppy-{5}-peppy = 144° | |
xox3xxx5oxo&#xt | tiatidbicu | blend of 2tiatids | atpecu-{10}-pecu = 144° attricu-{3}-tricu = arccos(1/4) = 75.522488° | |
ooo3oxo5xox&#xt | doaid bicu | blend of 2doaids | attet-{3}-tet = arccos[-(1+3 sqrt(5))/8] = 164.477512° atpap-{5}-pap = 144° | |
xxx3oxo5xox&#xt | sridatibcu | blend of 2sridatis | attricu-{6}-tricu = arccos[-(1+3 sqrt(5))/8] = 164.477512° atpap-{5}-pap = 144° | |
ooo3oxx5xoo&#xt | edoaid | blend ofdoaid andiddip | attet-{3}-trip = arccos(-sqrt[9+3 sqrt(5)]/4) = 172.238756° atpap-{5}-pip = 162° | |
xxx3oxx5xoo&#xt | esridati | blend ofsridati andtipe | athip-{6}-tricu = arccos(-sqrt[9+3 sqrt(5)]/4) = 172.238756° atpap-{5}-pip = 162° | |
ooo3xox5ofx&#xt | biscrahi | (across. o5f) = 180° resulting in lacingpero | ||
xxx3xox5ofx&#xt | arse biscrahi | (acrossx . f) = 180° resulting in lacingpip (across. o5f) = 180° resulting in lacingpero attricu-{3}-tricu = arccos[-(1+3 sqrt(5))/8] = 164.477512° | ||
xfo3oox5ooo&#xt | iku | (acrossf3o .) = 180° resulting in lacingteddi | ||
xfo3oox5xxx&#xt | sridatidu | (acrossf3o .) = 180° resulting in lacingteddi (acrossf . x) = 180° resulting in lacingpip atpecu-{5}-pip = 162° | ||
xux3oox5ooo&#xt | iktum | (acrossu3o .) = 180° resulting in lacingtut | ||
xux3oox5xxx&#xt | srida gridtum | (acrossu3o .) = 180° resulting in lacingtut (acrossu . x) = 180° resulting in lacinghip atpecu-{5}-pip = 162° | ||
oAo3ooo5xox&#xt | owaudope | A = 3/sqrt(5) = 1.341641 | - | |
oAo3xxx5xox&#xt | twagy tiddip | A = 3/sqrt(5) = 1.341641 | atpecu-{5}-pecu = 144° | |
xBx3ooo5xox&#xt | twau sriddip | B = (5+3 sqrt(5))/5 = 2.341641 | - | |
xBx3xxx5xox&#xt | twagy griddip | B = (5+3 sqrt(5))/5 = 2.341641 | atpecu-{5}-pecu = 144° | |
ofo3oox5xoo&#xt | twau doaid | - | ||
xFx3oox5xoo&#xt | twau sridati | - | ||
ofo3xox5ooo&#xt | twau iddip | - | ||
ofo3xox5xxx&#xt | twau tiddip | atpecu-{5}-pecu = 144° | ||
xFx3xox5ooo&#xt | twau tipe | - | ||
xFx3xox5xxx&#xt | twau griddip | atpecu-{5}-pecu = 144° | ||
sys3sos5sos&#xt | twausniddip | y ≈ 2.253679 | - | |
| ... | ||||
| Stott Type | Lace Tower | Polychoron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oxo oox3oxo&#xt | rap | blend oftrippy andtraf | atsquippy-{4}-squippy = 180° resulting in lacingoct atoct-{3}-tet = arccos(-1/4) = 104.477512° | |
oxo oxo3ooo&#xt | tript | blend of 2trippies | atsquippy-{4}-squippy = arccos(-2/3) = 131.810315° attet-{3}-tet = arccos(-1/4) = 104.477512° | |
oxo oxo3xxx&#xt | tripuf bicu | blend of 2tripufs | atsquippy-{4}-squippy = arccos(-2/3) = 131.810315° attricu-{6}-tricu = arccos(-1/4) = 104.477512° attrip-{4}-trip = arccos(-1/9) = 96.379370° | |
oxx oxo3ooo&#xt | autepe | blend oftrippy andtepe | attet-{3}-tet = arccos[-sqrt(5/8)] = 142.238756° atsquippy-{4}-trip = arccos[-sqrt((41-4 sqrt(10))/54)] = 136.433934° | |
oxx oxo3xxx&#xt | triahipatrip | blend oftripuf andtricupe | attricu-{6}-tricu = arccos[-sqrt(5/8)] = 142.238756° atsquippy-{4}-trip = arccos[-sqrt((41-4 sqrt(10))/54)] = 136.433934° atcube-{4}-trip = arccos[-sqrt((32-21 sqrt(2))/46)] = 102.925295° | |
oxx oxx3ooo&#xt | etrippy | blend oftrippy andtisdip | atcube-{4}-squippy = arccos[-sqrt(5/6)] = 155.905157° attet-{3}-trip = arccos[-sqrt(5/8)] = 142.238756° | |
oxx oxx3xxx&#xt | etripuf | blend oftripuf andshiddip | atcube-{4}-squippy = arccos[-sqrt(5/6)] = 155.905157° athip-{6}-tricu = arccos[-sqrt(5/8)] = 142.238756° atcube-{4}-trip = arccos[-sqrt(5)/3] = 138.189685° | |
oxx xxo3ooo&#xt | (?) | blend oftepe andtriddip | attrip-{4}-sqtripuippy = arccos[-sqrt(8)/3] = 160.528779° attet-{3}-trip = 150° | |
oxx xxo3xxx&#xt | (?) | blend ofthiddip andtricupe | ... | |
oqo oox3xoo&#xt | hex | - | ||
oCo ooo3oox&#xt | tete | C = sqrt(5/2) = 1.581139 | - | |
oCo xxx3oox&#xt | tracufbil | C = sqrt(5/2) = 1.581139 | attrip-{3}-tricu = arccos(sqrt[3/8]) = 52.238756° | |
x(ou)x o(xo)x3x(xo)o&#xt | spid | (across(..) (xo)3(..)) = 180° resulting in lacingtrip (across(..) (..)3(xo)) = 180° resulting in lacingtrip | ||
x(ou)x o(ox)x3x(uo)x&#xt | biscsrip | (across(ou) (..)3(uo)) = 180° resulting in lacingco (across(..) (ox)3(..)) = 180° resulting in lacingtrip atoct-{3}-tricu = arccos(-1/4) = 104.477512° | ||
oso2oso3oso&#xt | hex | blend of 2octpies | attet-{3}-tet = 120° | |
| ... | ||||
oqo xxx3ooo&#xt | tisdip | attrip-{3}-trip = 90° | ||
oqo xxx3xxx&#xt | shiddip | athip-{6}-hip = 90° | ||
ofx xxx3ooo&#xt | trapedip | attrip-{3}-trip = 108° | ||
ofx xxx3xxx&#xt | phiddip | athip-{6}-hip = 108° | ||
xux xxx3ooo&#xt | thiddip | attrip-{3}-trip = 120° | ||
xux xxx3xxx&#xt | hiddip | athip-{6}-hip = 120° | ||
xxx oox3xux&#xt | tuttip | (acrossx . u) = 180° resulting in lacinghip (across. o3u) = 180° resulting in lacingtut | ||
xxx oxo3ooo&#xt | tridpyp | blend of 2tepes | attet-{3}-tet = 180° resulting in lacingtridpy attrip-{3}-trip = arccos(-7/9) = 141.057559° | |
xxx oxo3xxx&#xt | tobcupe | blend of 2tricupes | attricu-{6}-tricu = 180° resulting in lacingtobcu attrip-{3}-trip = arccos(-7/9) = 141.057559° atcube-{4}-cube = arccos(-1/3) = 109.471221° | |
xxx oxx3xxo&#xt | cope | blend of 2 gyratedtricupes | attricu-{6}-tricu = 180° resulting in lacingco atcube-{4}-trip = arccos[-1/sqrt(3)] = 125.264390° | |
xxx oxx3ooo&#xt | etepe | blend oftepe andtisdip | attet-{3}-trip = 180° resulting in lacingetripy atcube-{4}-trip = arccos[-sqrt(8)/3] = 160.528779° | |
xxx oxx3xxx&#xt | etcupe | blend oftricupe andshiddip | athip-{6}-tricu = 180° resulting in lacingetcu atcube-{4}-trip = arccos[-sqrt(8)/3] = 160.528779° atcube-{4}-cube = arccos[-sqrt(2/3)] = 144.735610° | |
xxx ofx3xoo&#xt | teddipe | (acrossx f .) = 180° resulting in lacingpip (across. f3o) = 180° resulting in lacingteddi | ||
xxx oAo3xox&#xt | tautipip | A = (1+sqrt(6))/2 = 1.724745 | - | |
xxx xBx3xox&#xt | tauhipip | B = (3+sqrt(6))/2 = 2.724745 | - | |
xxx oxo6sox&#xt | gyetcupe | blend oftricupe andhappip | athap-{6}-tricu = 180° resulting in lacinggyetcu attrip-{3}-trip ≈ 169.428208° atcube-{4}-trip ≈ 153.635039° | |
| Stott Type | Lace Tower | Polychoron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oxo oxo4ooo&#xt | cute | blend of 2cubpies | atsquippy-{4}-squippy = 90° | |
oxo oxo4xxx&#xt | squipuf bicu | blend of 2squipuf andtes | atsquacu-{8}-squacu = 90° atsquippy-{4}-squippy = 90° attrip-{4}-trip = arccos(1/3) = 70.528779° | |
oyo oox4xoo&#xt | squapt | y = sqrt[2-1/sqrt(2)] = 1.137055 | - | |
oxx oxx4ooo&#xt | ecubpy | blend ofcubpy andtes | atsquippy-{4}-squippy = 135° | |
oxx oxx4xxx&#xt | esquipuf | blend ofsquipuf andsodip | atcube-{4}-squippy = 135° atop-{8}-squacu = 135° atcube-{4}-trip = arccos[-1/sqrt(3)] = 125.264390° | |
xox oxo4ooo&#xt | hex | - | ||
xox oxo4xxx&#xt | quawros | - | ||
xox xox4oqo&#xt | cytau tes | - | ||
xox xox4xwx&#xt | cyte cubau sodip | - | ||
o(qo)o o(ox)o4o(oo)o&#xt | hex | blend of 2octpies | attet-{3}-tet = 120° | |
o(qo)o o(ox)o4x(xx)x&#xt | quawros | blend of 2squacufbils | attet-{3}-tet = 120° attrip-{4}-trip = arccos(-1/3) = 109.471221° atcube-{4}-cube = 90° | |
x(wx)x o(ox)o4o(oo)o&#xt | pex hex | blend of 2esquippidpies | attet-{3}-tet = 120° attrip-{4}-trip = arccos(-1/3) = 109.471221° | |
x(wx)x o(ox)o4x(xx)x&#xt | pacsid pith | blend of 2cubasircoes | attet-{3}-tet = 120° attrip-{4}-trip = arccos(-1/3) = 109.471221° atcube-{4}-cube = 90° | |
(qo)q(qo) (ox)x(ox)4(oo)o(oo)&#xt | cytau tes | (acrossq x .) = 180° resulting in lacingcube atsquippy-{4}-squippy = 180° resulting in lacingoct | ||
(qo)q(qo) (ox)x(ox)4(xx)x(xx)&#xt | cyte opau sodip | (acrossq x .) = 180° resulting in lacingcube (acrossq . x) = 180° resulting in lacingcube atsquacu-{8}-squacu = 180° resulting in lacingsquobcu | ||
(qo)q(qo) (xo)o(xo)4(oq)q(oq)&#xt | rit | (across. o4q) = 180° resulting in lacingco | ||
(qo)(qo)(qo) (ox)(xo)(ox)4(oo)(oq)(oo)&#xt | ico | blend of 2octacoes | atsquippy-{4}-squippy = 180° resulting in lacingoct atoct-{3}-oct = 120° | |
(qo)(qo)(qo) (ox)(xo)(ox)4(xx)(xw)(xx)&#xt | bicyte ausodip | (across(qo) (..) (xw)) = 180° resulting in lacingesquidpy atsquacu-{8}-squacu = 180° resulting in lacingsquobcu atoct-{3}-oct = 120° | ||
(wx)(wx)(wx) (ox)(xo)(ox)4(oo)(oq)(oo)&#xt | pexic | (across(wx) (..) (oq)) = 180° resulting in lacingesquidpy atsquippy-{4}-squippy = 180° resulting in lacingoct atoct-{3}-oct = 120° | ||
(wx)(wx)(wx) (ox)(xo)(ox)4(xx)(xw)(xx)&#xt | pacsrit | blend of 2sircoatics | atsquacu-{8}-squacu = 180° resulting in lacingsquobcu atoct-{3}-oct = 120° | |
oso2oso4oso&#xt | squapt | blend of 2squappies | atsquippy-{4}-squippy = arccos[-(2-sqrt(2))/2] = 107.031248° attet-{3}-tet = arccos[(3 sqrt(2)-4)/8] = 88.261948° | |
| ... | ||||
oqo xxx4ooo&#xt | tes | (acrossq x .) = 180° resulting in lacingcube atcube-{4}-cube = 90° | ||
oqo xxx4xxx&#xt | sodip | (acrossq x .) = 180° resulting in lacingcube (acrossq . x) = 180° resulting in lacingcube atop-{8}-op = 90° | ||
ofx xxx4ooo&#xt | squipdip | (acrossf x .) = 180° resulting in lacingpip atcube-{4}-cube = 108° | ||
ofx xxx4xxx&#xt | podip | (acrossf x .) = 180° resulting in lacingpip (acrossf . x) = 180° resulting in lacingpip atop-{8}-op = 108° | ||
xux xxx4ooo&#xt | shiddip | (acrossu x .) = 180° resulting in lacinghip atcube-{4}-cube = 120° | ||
xux xxx4xxx&#xt | hodip | (acrossu x .) = 180° resulting in lacinghip (acrossu . x) = 180° resulting in lacinghip atop-{8}-op = 120° | ||
xxx oox4oxo&#xt | gyespyp | blend ofsquippyp andsquappip | atsquap-{4}-squippy = 180° resulting in lacinggyesp attrip-{4}-trip ≈ 158.571770° | |
xxx oxo4ooo&#xt | ope | blend of 2squippyps | atsquippy-{4}-squippy = 180° resulting in lacingoct attrip-{4}-trip = arccos(-1/3) = 109.471221° | |
xxx oxo4xxx&#xt | squobcupe | blend of 2squacupes | atsquacu-{8}-squacu = 180° resulting in lacingsquobcu attrip-{4}-trip = arccos(-1/3) = 109.471221° atcube-{4}-cube = 90° | |
xxx oxx4xxo&#xt | squigybcupe | blend of 2 gyratedsquacupes | atsquacu-{8}-squacu = 180° resulting in lacingsquigybcu atcube-{4}-trip = arccos(-sqrt[(3-2 sqrt(2))/6]) = 99.735610° | |
xxx oxx4ooo&#xt | esquipyp | blend ofsquippyp andtes | atcube-{4}-squippy = 180° resulting in lacingesquipy atcube-{4}-trip = arccos[-sqrt(2/3)] = 144.735610° | |
xxx oxx4xxx&#xt | escupe | blend ofsquacupe andsodip | atop-{8}-squacu = 180° resulting in lacingescu atcube-{4}-trip = arccos[-sqrt(2/3)] = 144.735610° atcube-{4}-cube = 135° | |
xxx oqo4xox&#xt | cope | (acrossx q .) = 180° resulting in lacingcube (across. q4o) = 180° resulting in lacingco | ||
xxx oxo8sox&#xt | gyescupe | blend ofsquacupe andoappip | atoap-{8}-squacu = 180° resulting in lacinggyescu attrip-{4}-trip ≈ 151.330128° atcube-{4}-trip ≈ 141.594518° | |
| Stott Type | Lace Tower | Polychoron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
ovo oox5xoo&#xt | papt | v = (sqrt(5)-1)/2 = 0.618034 | - | |
oxo oxo5ooo&#xt | pipt | blend of 2pippies | atpeppy-{5}-peppy = 36° atsquippy-{4}-squippy = arccos(2/sqrt(5)) = 26.565051° | |
oxo oxo5xxx&#xt | pepuf bicu | blend of 2pepufs | atpecu-{10}-pecu = 36° atsquippy-{4}-squippy = arccos(2/sqrt(5)) = 26.565051° attrip-{4}-trip = arccos[(5+4 sqrt(5))/15] = 21.624634° | |
oxx oxx5ooo&#xt | epippy | blend ofpippy andsquipdip | atpeppy-{5}-pip = 108° atcube-{4}-squippy = arccos(sqrt[(5-2 sqrt(5))/10]) = 103.282526°° | |
oxx oxx5xxx&#xt | epepuf | blend ofpepuf andsquadedip | atdip-{10}-pecu = 108° atcube-{4}-squippy = arccos(sqrt[(5-2 sqrt(5))/10]) = 103.282526° atcube-{4}-trip = arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317° | |
oso2oso5oso&#xt | papt | blend of 2pappies | atpeppy-{5}-peppy = 72° attet-{3}-tet = arccos[(3 sqrt(5)-1)/8] = 44.477512° | |
| ... | ||||
oqo xxx5ooo&#xt | squipdip | (acrossq x .) = 180° resulting in lacingcube atpip-{5}-pip = 90° | ||
oqo xxx5xxx&#xt | squadedip | (acrossq x .) = 180° resulting in lacingcube (acrossq . x) = 180° resulting in lacingcube atdip-{10}-dip = 90° | ||
ofx xxx5ooo&#xt | pedip | (acrossf x .) = 180° resulting in lacingpip atpip-{5}-pip = 108° | ||
ofx xxx5xxx&#xt | padedip | (acrossf x .) = 180° resulting in lacingpip (acrossf . x) = 180° resulting in lacingpip atdip-{10}-dip = 108° | ||
xux xxx5ooo&#xt | phiddip | (acrossu x .) = 180° resulting in lacinghip atpip-{5}-pip = 120° | ||
xux xxx5xxx&#xt | hadedip | (acrossu x .) = 180° resulting in lacinghip (acrossu . x) = 180° resulting in lacinghip atdip-{10}-dip = 120° | ||
xxx oox5oxo&#xt | gyepippip | blend ofpippy andpappip | atpap-{5}-peppy = 180° resulting in lacinggeypip attrip-{4}-trip = arccos(-sqrt(5)/3) = 138.189685° | |
xxx oxo5ooo&#xt | pedpyp | blend of 2peppyps | atpeppy-{5}-peppy = 180° resulting in lacingpedpy attrip-{4}-trip = arccos[(4 sqrt(5)-5)/15] = 74.754736° | |
xxx oxo5xxx&#xt | pobcupe | blend of 2pecupes | atpecu-{10}-pecu = 180° resulting in lacingpobcu attrip-{4}-trip = arccos[(4 sqrt(5)-5)/15] = 74.754736° atcube-{4}-cube = arccos(1/sqrt(5)) = 63.434949° | |
xxx oxx5xxo&#xt | pegybcupe | blend of 2 gyratedpecupes | atpecu-{10}-pecu = 180° resulting in lacingpegybcu atcube-{4}-trip = arccos(sqrt[(3-sqrt(5))/6]) = 69.094843° | |
xxx oxx5ooo&#xt | epeppyp | blend ofpeppyp andsquipdip | atpeppy-{5}-pip = 180° resulting in lacingepeppy atcube-{4}-trip = arccos(-sqrt[(10-2 sqrt(5))/15]) = 127.377368° | |
xxx oxx5xxx&#xt | epcupe | blend ofpecupe andsquadedip | atdip-{10}-pecu = 180° resulting in lacingepcu atcube-{4}-trip = arccos(-sqrt[(10-2 sqrt(5))/15]) = 127.377368° atcube-{4}-cube = arccos(-sqrt[(5-sqrt(5))/10]) = 121.717474° | |
xxx ofx5xox&#xt | perope | (acrossx f .) = 180° resulting in lacingpip (across. f5o) = 180° resulting in lacingpero | ||
xxx oxo10sox&#xt | gyepcupe | blend ofpecupe anddappip | atdap-{10}-pecu = 180° resulting in lacinggyepcu attrip-{4}-trip ≈ 132.624012° atcube-{4}-trip ≈ 126.964118° | |
| Stott Type | Lace Tower | Polychoron | Remarks | Equatorial Dihedral Angles |
|---|---|---|---|---|
oxo oxo oxo&#xt | cute | blend of 2cubpies | atsquippy-{4}-squippy = 90° | |
oxo oxo xox&#xt | hex | - | ||
oxo xox xox&#xt | cute | - | ||
oao oox xoo&#xt | tete | a = sqrt(5/2) = 1.581139 | - | |
oso2oso2oso&#xt | tete | blend of 2pens | attet-{3}-tet = arccos(-7/8) = 151.044976° | |
| ... | ||||
oox oyo xxx&#xt | tridpyp | y = sqrt(8/3) = 1.632993 | - | |
oox xYx xxx&#xt | etidpyp | Y = sqrt[(11+4 sqrt(6))/3] = 2.632993 | - | |
oxo oxo xxx&#xt | ope | blend of 2squippyps | atsquippy-{4}-squippy = 180° resulting in lacingoct attrip-{4}-trip = arccos(-1/3) = 109.471221° | |
oxo oxx xxx&#xt | autipip | blend ofsquippyp andtisdip | atsquippy-{4}-trip = 180° resulting in lacingautip attrip-{4}-trip = arccos[-sqrt(2/3)] = 144.735610° atcube-{4}-trip = arccos[-(sqrt(6)-1)/sqrt(12)] = 114.735610° | |
oxx xxo xxx&#xt | gybeffip | blend of 2 gyratedtisdips | attrip-{4}-trip = 180° resulting in lacinggybef atcube-{4}-trip = 150° | |
oqo xxx xxx&#xt | tes | (acrossq x .) = 180° resulting in lacingcube (acrossq . x) = 180° resulting in lacingcube atcube-{4}-cube = 90° | ||
ofx xxx xxx&#xt | squipdip | (acrossf x .) = 180° resulting in lacingpip (acrossf . x) = 180° resulting in lacingpip atcube-{4}-cube = 108° | ||
oAx xox xxx&#xt | bautipip | A = (1+sqrt(6))/2 = 1.724745 | - | |
xox oqo xxx&#xt | ope | - | ||
xox xwx xxx&#xt | esquidpyp | - | ||
xux xxx xxx&#xt | shiddip | (acrossu x .) = 180° resulting in lacinghip (acrossu . x) = 180° resulting in lacinghip atcube-{4}-cube = 120° | ||
o(ox)o o(ox)o x(wx)x&#xt | pex hex | blend of 2esquippidpies | attet-{3}-tet = 120° attrip-{4}-trip = arccos(-1/3) = 109.471221° | |
o(qo)o o(oq)o x(xx)x&#xt | ope | blend of 2squippyps | atsquippy-{4}-squippy = 180° resulting in lacingoct attrip-{4}-trip = arccos(-1/3) = 109.471221° | |
o(qo)o x(xw)x x(xx)x&#xt | esquidpyp | (across(qo) (xw) (..)) = 180° resulting in lacingesquidpy attrip-{4}-trip = arccos(-1/3) = 109.471221° atcube-{4}-cube = 90° | ||
x(wx)x x(xw)x x(xx)x&#xt | squobcupe | blend of 2squacupes | (across(wx) (xw) (..)) = 180° resulting in lacingsquobcu attrip-{4}-trip = arccos(-1/3) = 109.471221° atcube-{4}-cube = 90° | |
o(qoo)o o(oqo)o o(ooq)o&#xt | hex | blend of 2octpies | attet-{3}-tet = 120° | |
o(qoo)o o(oqo)o x(xxw)x&#xt | pex hex | blend of 2esquippidpies | attet-{3}-tet = 120° attrip-{4}-trip = arccos(-1/3) = 109.471221° | |
o(qoo)o x(xwx)x x(xxw)x&#xt | quawros | blend of 2squacufbils | attet-{3}-tet = 120° attrip-{4}-trip = arccos(-1/3) = 109.471221° atcube-{4}-cube = 90° | |
x(wxx)x x(xwx)x x(xxw)x&#xt | pacsid pith | blend of 2cubasircoes | attet-{3}-tet = 120° attrip-{4}-trip = arccos(-1/3) = 109.471221° atcube-{4}-cube = 90° | |
(xu)o(xu) (ho)B(ho) (xx)x(xx)&#xt | pabaushiddip | B = sqrt(3)+sqrt(2) = 3.146264 | - | |
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