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Cantellated 7-cubes

Orthogonal projections in B6 Coxeter plane

In seven-dimensional geometry, a cantellated 7-cube is a convex uniform 7-polytope, being a cantellation of the regular 7-cube.

There are 10 degrees of cantellation for the 7-cube, including truncations. 4 are most simply constructible from the dual 7-orthoplex.

Cantellated 7-cube

Cantellated 7-cube
Type
Schläfli symbol
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Small rhombated hepteract (acronym: sersa) (Jonathan Bowers)

Images

Bicantellated 7-cube

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

Alternate names

  • Small birhombated hepteract (acronym: sibrosa) (Jonathan Bowers)

Images

Tricantellated 7-cube

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

Alternate names

  • Small trirhombihepteractihecatonicosoctaexon (acronym: strasaz) (Jonathan Bowers)

Images

Cantitruncated 7-cube

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

Alternate names

  • Great rhombated hepteract (acronym: gersa) (Jonathan Bowers)

Images

It is fifth in a series of cantitruncated hypercubes:

Bicantitruncated 7-cube

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

Alternate names

  • Great birhombated hepteract (acronym: gibrosa) (Jonathan Bowers)

Images

Tricantitruncated 7-cube

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

Alternate names

  • Great trirhombihepteractihecatonicosoctaexon (acronym: gotrasaz) (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, http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html
      • (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.
  • x3o3x3o3o3o4o- sersa, o3x3o3x3o3o4o - sibrosa, o3o3x3o3x3o4o - strasaz, x3x3x3o3o3o4o - gersa, o3x3x3x3o3o4o - gibrosa, o3o3x3x3x3o4o - gotrasaz

References

  1. Klitizing, (x3o3x3o3o3o4o - sersa)
  2. Klitizing, (o3x3o3x3o3o4o - sibrosa)
  3. Klitizing, (o3o3x3o3x3o4o - strasaz)
  4. Klitizing, (x3x3x3o3o3o4o - gersa)
  5. Klitizing, (o3x3x3x3o3o4o - gibrosa)
  6. Klitizing, (o3o3x3x3x3o4o - gotrasaz)
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