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Stericated 7-cubes

From Wikipedia, the free encyclopedia
(Redirected fromSteriruncinated 7-cube)
Orthogonal projections in B6Coxeter plane

7-cube

Stericated 7-cube

Bistericated 7-cube

Steritruncated 7-cube

Bisteritruncated 7-cube

Stericantellated 7-cube

Bistericantellated 7-cube

Stericantitruncated 7-cube

Bistericantitruncated 7-cube

Steriruncinated 7-cube

Steriruncitruncated 7-cube

Steriruncicantellated 7-cube

Bisteriruncitruncated 7-cube

Steriruncicantitruncated 7-cube

Bisteriruncicantitruncated 7-cube

In seven-dimensionalgeometry, astericated 7-cube is a convexuniform 7-polytope with 4th-ordertruncations (sterication) of the regular7-cube.

There are 24 unique sterication for the 7-cube with permutations of truncations, cantellations, and runcinations. 10 are more simply constructed from the7-orthoplex.

This polytope is one of 127uniform 7-polytopes with B7 symmetry.

Stericated 7-cube

[edit]
Stericated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Small cellated hepteract (acronym: ) (Jonathan Bowers)[1]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Bistericated 7-cube

[edit]
bistericated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Small bicellated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)[2]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Steritruncated 7-cube

[edit]
steritruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Cellitruncated hepteract (acronym: ) (Jonathan Bowers)[3]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Bisteritruncated 7-cube

[edit]
bisteritruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Bicellitruncated hepteract (acronym: ) (Jonathan Bowers)[4]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Stericantellated 7-cube

[edit]
Stericantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,2,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Cellirhombated hepteract (acronym: ) (Jonathan Bowers)[5]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Bistericantellated 7-cube

[edit]
Bistericantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,3,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Bicellirhombihepteract (acronym: ) (Jonathan Bowers)[6]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Stericantitruncated 7-cube

[edit]
stericantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Celligreatorhombated hepteract (acronym: ) (Jonathan Bowers)[7]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Bistericantitruncated 7-cube

[edit]
bistericantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,3,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Bicelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)[8]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Steriruncinated 7-cube

[edit]
Steriruncinated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Celliprismated hepteract (acronym: ) (Jonathan Bowers)[9]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Steriruncitruncated 7-cube

[edit]
steriruncitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Celliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)[10]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Steriruncicantellated 7-cube

[edit]
steriruncicantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,2,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Celliprismatorhombated hepteract (acronym: ) (Jonathan Bowers)[11]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Bisteriruncitruncated 7-cube

[edit]
bisteriruncitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,4,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Bicelliprismatotruncated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)[12]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Steriruncicantitruncated 7-cube

[edit]
steriruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Great cellated hepteract (acronym: ) (Jonathan Bowers)[13]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graph
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graphtoo complextoo complex
Dihedral symmetry[6][4]

Bisteriruncicantitruncated 7-cube

[edit]
bisteriruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,3,4,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

[edit]
  • Great bicellated hepteractihecatonicosoctaexon (Acronym ) (Jonathan Bowers)[14]

Images

[edit]
orthographic projections
Coxeter planeB7 / A6B6 / D7B5 / D6 / A4
Graphtoo complex
Dihedral symmetry[14][12][10]
Coxeter planeB4 / D5B3 / D4 / A2B2 / D3
Graph
Dihedral symmetry[8][6][4]
Coxeter planeA5A3
Graph
Dihedral symmetry[6][4]

Notes

[edit]
  1. ^Klitizing, (x3o3o3o3x3o4o - )
  2. ^Klitizing, (x3o3x3o3x3o4o - )
  3. ^Klitizing, (x3x3o3o3x3o4o - )
  4. ^Klitizing, (o3x3x3o3o3x4o - )
  5. ^Klitizing, (x3o3x3o3x3o4o - )
  6. ^Klitizing, (o3x3o3x3o3x4o - )
  7. ^Klitizing, (x3x3x3o3x3o4o - )
  8. ^Klitizing, (o3x3x3x3o3x4o - )
  9. ^Klitizing, (x3o3o3x3x3o4o - )
  10. ^Klitizing, (x3x3x3o3x3o4o - )
  11. ^Klitizing, (x3o3x3x3x3o4o - )
  12. ^Klitizing, (o3x3x3o3x3x4o - )
  13. ^Klitizing, (x3x3x3x3x3o4o - )
  14. ^Klitizing, (o3x3x3x3x3x4o - )

References

[edit]
  • H.S.M. Coxeter:
    • H.S.M. Coxeter,Regular Polytopes, 3rd Edition, Dover New York, 1973
    • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,wiley.com,ISBN 978-0-471-01003-6
      • (Paper 22) H.S.M. Coxeter,Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
      • (Paper 23) H.S.M. Coxeter,Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
      • (Paper 24) H.S.M. Coxeter,Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • Norman JohnsonUniform Polytopes, Manuscript (1991)
    • N.W. Johnson:The Theory of Uniform Polytopes and Honeycombs, Ph.D.
  • Klitzing, Richard."7D uniform polytopes (polyexa)". x3o3o3o3x3o4o - , x3o3x3o3x3o4o - , x3x3o3o3x3o4o - , o3x3x3o3o3x4o - , x3o3x3o3x3o4o - , o3x3o3x3o3x4o - , x3x3x3o3x3o4o - , o3x3x3x3o3x4o - , x3o3o3x3x3o4o - , x3x3x3o3x3o4o - , x3o3x3x3x3o4o - , o3x3x3o3x3x4o - , x3x3x3x3x3o4o - , o3x3x3x3x3x4o -

External links

[edit]
Fundamental convexregular anduniform polytopes in dimensions 2–10
FamilyAnBnI2(p) /DnE6 /E7 /E8 /F4 /G2Hn
Regular polygonTriangleSquarep-gonHexagonPentagon
Uniform polyhedronTetrahedronOctahedron •CubeDemicubeDodecahedron •Icosahedron
Uniform polychoronPentachoron16-cell •TesseractDemitesseract24-cell120-cell •600-cell
Uniform 5-polytope5-simplex5-orthoplex •5-cube5-demicube
Uniform 6-polytope6-simplex6-orthoplex •6-cube6-demicube122 •221
Uniform 7-polytope7-simplex7-orthoplex •7-cube7-demicube132 •231 •321
Uniform 8-polytope8-simplex8-orthoplex •8-cube8-demicube142 •241 •421
Uniform 9-polytope9-simplex9-orthoplex •9-cube9-demicube
Uniform 10-polytope10-simplex10-orthoplex •10-cube10-demicube
Uniformn-polytopen-simplexn-orthoplex •n-cuben-demicube1k2 •2k1 •k21n-pentagonal polytope
Topics:Polytope families •Regular polytope •List of regular polytopes and compounds •Polytope operations
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