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Pentellated 7-cubes


In seven-dimensional geometry, a pentellated 7-cube is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-cube. There are 32 unique pentellations of the 7-cube with permutations of truncations, cantellations, runcinations, and sterications. 16 are more simply constructed relative to the 7-orthoplex.

[[File:7-cube t012345 B6.svg120px]]
Pentisteriruncicantitruncated 7-cube

Pentellated 7-cube

Pentellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Small terated hepteract (acronym: stesa) (Jonathan Bowers)

Images

Pentitruncated 7-cube

pentitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Teritruncated hepteract (acronym: tetsa) (Jonathan Bowers)

Images

Penticantellated 7-cube

Penticantellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Terirhombated hepteract (acronym: tersa) (Jonathan Bowers)

Images

Penticantitruncated 7-cube

penticantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Terigreatorhombated hepteract (acronym: togresa) (Jonathan Bowers)

Images

Pentiruncinated 7-cube

pentiruncinated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Teriprismated hepteract (acronym: tapsa) (Jonathan Bowers)

Images

Pentiruncitruncated 7-cube

pentiruncitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Teriprismatotruncated hepteract (acronym: toptasa) (Jonathan Bowers)

Images

Pentiruncicantellated 7-cube

pentiruncicantellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Teriprismatorhombated hepteract (acronym: topresa) (Jonathan Bowers)

Images

Pentiruncicantitruncated 7-cube

pentiruncicantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Terigreatoprismated hepteract (acronym: togapsa) (Jonathan Bowers)

Images

Pentistericated 7-cube

pentistericated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Tericellated hepteract (acronym: tacosa) (Jonathan Bowers)

Images

Pentisteritruncated 7-cube

pentisteritruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Tericellitruncated hepteract (acronym: tecatsa) (Jonathan Bowers)

Images

Pentistericantellated 7-cube

pentistericantellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Tericellirhombated hepteract (acronym: tecresa) (Jonathan Bowers)

Images

Pentistericantitruncated 7-cube

pentistericantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Tericelligreatorhombated hepteract (acronym: tecgresa) (Jonathan Bowers)

Images

Pentisteriruncinated 7-cube

Pentisteriruncinated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Bipenticantitruncated 7-cube as t1,2,3,6{4,35}
  • Tericelliprismated hepteract (acronym: tecpasa) (Jonathan Bowers)

Images

Pentisteriruncitruncated 7-cube

pentisteriruncitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Tericelliprismatotruncated hepteract (acronym: tecpetsa) (Jonathan Bowers)

Images

Pentisteriruncicantellated 7-cube

pentisteriruncicantellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Bipentiruncicantitruncated 7-cube as t1,2,3,4,6{4,35}
  • Tericelliprismatorhombated hepteract (acronym: tocpresa) (Jonathan Bowers)

Images

Pentisteriruncicantitruncated 7-cube

pentisteriruncicantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Great terated hepteract (acronym: gotesa) (Jonathan Bowers)

Images

Notes

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, wiley.com,
      • (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.

References

  1. Klitzing, (x4o3o3o3o3x3o - stesa)
  2. Klitzing, (x4x3o3o3o3x3o - tetsa)
  3. Klitzing, (x4o3x3o3o3x3o - tersa)
  4. Klitzing, (x4x3x3o3o3x3o - togresa)
  5. Klitzing, (x4o3o3x3o3x3o - tapsa)
  6. Klitzing, (x4x3o3x3o3x3o - toptasa)
  7. Klitzing, (x4o3x3x3o3x3o - topresa)
  8. Klitzing, (x4x3x3x3o3x3o - togapsa)
  9. Klitzing, (x4o3o3o3x3x3o - tacosa)
  10. Klitzing, (x4x3o3o3x3x3o - tecatsa)
  11. Klitzing, (x4o3x3o3x3x3o - tecresa)
  12. Klitzing, (x4x3x3o3x3x3o - tecgresa)
  13. Klitzing, (x4o3o3x3x3x3o - tecpasa)
  14. Klitzing, (x4x3o3x3x3x3o - tecpetsa)
  15. Klitzing, (x4o3x3x3x3x3o - tocpresa)
  16. Klitzing, (x4x3x3x3x3x3o - gotesa)
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