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Stericated 7-cubes

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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

Stericated 7-cube
Type uniform 7-polytope
Schläfli symbol t0,4{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Small cellated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Bistericated 7-cube

bistericated 7-cube
Type uniform 7-polytope
Schläfli symbol t1,5{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Small bicellated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Steritruncated 7-cube

steritruncated 7-cube
Type uniform 7-polytope
Schläfli symbol t0,1,4{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Cellitruncated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Bisteritruncated 7-cube

bisteritruncated 7-cube
Type uniform 7-polytope
Schläfli symbol t1,2,5{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Bicellitruncated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Stericantellated 7-cube

Stericantellated 7-cube
Type uniform 7-polytope
Schläfli symbol t0,2,4{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Cellirhombated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Bistericantellated 7-cube

Bistericantellated 7-cube
Type uniform 7-polytope
Schläfli symbol t1,3,5{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Bicellirhombihepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Stericantitruncated 7-cube

stericantitruncated 7-cube
Type uniform 7-polytope
Schläfli symbol t0,1,2,4{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Celligreatorhombated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Bistericantitruncated 7-cube

bistericantitruncated 7-cube
Type uniform 7-polytope
Schläfli symbol t1,2,3,5{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Bicelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Steriruncinated 7-cube

Steriruncinated 7-cube
Type uniform 7-polytope
Schläfli symbol t0,3,4{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Celliprismated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Steriruncitruncated 7-cube

steriruncitruncated 7-cube
Type uniform 7-polytope
Schläfli symbol t0,1,3,4{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Celliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Steriruncicantellated 7-cube

steriruncicantellated 7-cube
Type uniform 7-polytope
Schläfli symbol t0,2,3,4{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Celliprismatorhombated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Bisteriruncitruncated 7-cube

bisteriruncitruncated 7-cube
Type uniform 7-polytope
Schläfli symbol t1,2,4,5{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Bicelliprismatotruncated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Steriruncicantitruncated 7-cube

steriruncicantitruncated 7-cube
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,4{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Great cellated hepteract (acronym: ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph too complex too complex
Dihedral symmetry

Bisteriruncicantitruncated 7-cube

bisteriruncicantitruncated 7-cube
Type uniform 7-polytope
Schläfli symbol t1,2,3,4,5{4,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7,
Properties convex

Alternate names

  • Great bicellated hepteractihecatonicosoctaexon (Acronym ) (Jonathan Bowers)

Images

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry
Coxeter plane A5 A3
Graph
Dihedral symmetry

Notes

  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

  • 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, ISBN 978-0-471-01003-6
      • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I,
      • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II,
      • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III,
  • Norman Johnson Uniform 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

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
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