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Stericated 7-cubes

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(Redirected from Steritruncated 7-cube)
Orthogonal projections in B6 Coxeter 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-dimensional geometry, a stericated 7-cube is a convex uniform 7-polytope with 4th-order truncations (sterication) of the regular 7-cube.

There are 24 unique sterication for the 7-cube with permutations of truncations, cantellations, and runcinations. 10 are more simply constructed from the 7-orthoplex. This polytope is one of 127 uniform 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: scosa) (Jonathan Bowers)[1]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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 hepteractihecatonicosaoctaexon (acronym: sabcosaz) (Jonathan Bowers)[2]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: catsa) (Jonathan Bowers)[3]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: bactasa) (Jonathan Bowers)[4]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: carsa) (Jonathan Bowers)[5]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: bacresaz) (Jonathan Bowers)[6]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: cogarsa) (Jonathan Bowers)[7]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: becgresa) (Jonathan Bowers)[8]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: capsa) (Jonathan Bowers)[9]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: captesa) (Jonathan Bowers)[10]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: copresa) (Jonathan Bowers)[11]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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 hepteractihecatonicosaoctaexon (acronym: bocaptosaz) (Jonathan Bowers)[12]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
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: gacosa) (Jonathan Bowers)[13]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph too complex too 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 hepteractihecatonicosaoctaexon (acronym: gabcosaz) (Jonathan Bowers) [14]

Images

[edit]
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Notes

[edit]
  1. ↑ Klitzing, (x4o3o3o3x3o3o - scosa)
  2. ↑ Klitzing, (o4x3o3o3o3x3o - sabcosaz)
  3. ↑ Klitzing, (x4x3o3o3x3o3o - catsa)
  4. ↑ Klitzing, (o4x3x3o3o3x3o - bactasa)
  5. ↑ Klitzing, (x4o3x3o3x3o3o - carsa)
  6. ↑ Klitzing, (o4x3o3x3o3x3o - bacresaz)
  7. ↑ Klitzing, (x4x3x3o3x3o3o - cogarsa)
  8. ↑ Klitzing, (o4x3x3x3o3x3o - becgresa)
  9. ↑ Klitzing, (x4o3o3x3x3o3o - capsa)
  10. ↑ Klitzing, (x4x3o3x3x3o3o - captesa)
  11. ↑ Klitzing, (x4o3x3x3x3o3o - copresa)
  12. ↑ Klitzing, (o4x3x3o3x3x3o - bocaptosaz)
  13. ↑ Klitzing, (x4x3x3x3x3o3o - gacosa)
  14. ↑ Klitzing, (o4x3x3x3x3x3o - gabcosaz)

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 Ivić 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 Johnson Uniform Polytopes, Manuscript (1991)
    • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
  • Klitzing, Richard. "7D uniform polytopes (polyexa) with acronyms".
[edit]
Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron
Uniform polychoron Pentachoron 16-cell • Tesseract Demitesseract 24-cell 120-cell • 600-cell
Uniform 5-polytope 5-simplex 5-orthoplex • 5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221
Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 • 231 • 321
Uniform 8-polytope 8-simplex 8-orthoplex • 8-cube 8-demicube 142 • 241 • 421
Uniform 9-polytope 9-simplex 9-orthoplex • 9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex • 10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplex • n-cube n-demicube 1k2 • 2k1 • k21 n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds • Polytope operations
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