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Cantellated 7-orthoplexes

Orthogonal projections in B6 Coxeter plane

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

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

Cantellated 7-orthoplex

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

Alternate names

  • Small rhombated hecatonicosoctaexon (acronym: sarz) (Jonathan Bowers)

Images

Bicantellated 7-orthoplex

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

Alternate names

  • Small birhombated hecatonicosoctaexon (acronym: sebraz) (Jonathan Bowers)

Images

Cantitruncated 7-orthoplex

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

Alternate names

  • Great rhombated hecatonicosoctaexon (acronym: garz) (Jonathan Bowers)

Images

Bicantitruncated 7-orthoplex

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

Alternate names

  • Great birhombated hecatonicosoctaexon (acronym: gebraz) (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. 1966
    • o3o3o3o3x3o4x - sarz, o3o3o3x3o3x4o - sebraz, o3o3o3o3x3x4x - garz, o3o3o3x3x3x4o - gebraz

References

  1. Klitizing, (o3o3o3o3x3o4x - sarz)
  2. Klitizing, (o3o3o3x3o3x4o - sebraz)
  3. Klitizing, (o3o3o3o3x3x4x - garz)
  4. Klitizing, (o3o3o3x3x3x4o - gebraz)
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