Cantellated_7-cube

Cantellated 7-cubes

Cantellated 7-cubes

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

More information Orthogonal projections in B6 Coxeter plane ...

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
Typeuniform 7-polytope
Schläfli symbolrr{4,3,3,3,3,3}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges16128
Vertices2688
Vertex figure
Coxeter groupsB7, [4,3,3,3,3,3]
Propertiesconvex

Alternate names

  • Small rhombated hepteract (acronym: sersa) (Jonathan Bowers)[1]

Images

More information Coxeter plane, B7 / A6 ...

Bicantellated 7-cube

More information Bicantellated 7-cube ...

Alternate names

  • Small birhombated hepteract (acronym: sibrosa) (Jonathan Bowers)[2]

Images

More information Coxeter plane, B7 / A6 ...

Tricantellated 7-cube

More information Tricantellated 7-cube ...

Alternate names

  • Small trirhombihepteractihecatonicosoctaexon (acronym: strasaz) (Jonathan Bowers)[3]

Images

More information Coxeter plane, B7 / A6 ...

Cantitruncated 7-cube

More information Cantitruncated 7-cube ...

Alternate names

  • Great rhombated hepteract (acronym: gersa) (Jonathan Bowers)[4]

Images

More information Coxeter plane, B7 / A6 ...

It is fifth in a series of cantitruncated hypercubes:

Petrie polygon projections
Truncated cuboctahedron Cantitruncated tesseract Cantitruncated 5-cube Cantitruncated 6-cube Cantitruncated 7-cube Cantitruncated 8-cube

Bicantitruncated 7-cube

More information Bicantitruncated 7-cube ...

Alternate names

  • Great birhombated hepteract (acronym: gibrosa) (Jonathan Bowers)[5]

Images

More information Coxeter plane, B7 / A6 ...

Tricantitruncated 7-cube

More information Tricantitruncated 7-cube ...

Alternate names

  • Great trirhombihepteractihecatonicosoctaexon (acronym: gotrasaz) (Jonathan Bowers)[6]

Images

More information Coxeter plane, B7 / A6 ...

These polytopes are from a family of 127 uniform 7-polytopes with B7 symmetry.

See also

Notes

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

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, [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)". x3o3x3o3o3o4o- sersa, o3x3o3x3o3o4o - sibrosa, o3o3x3o3x3o4o - strasaz, x3x3x3o3o3o4o - gersa, o3x3x3x3o3o4o - gibrosa, o3o3x3x3x3o4o - gotrasaz
More information Family, Regular polygon ...
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This article uses material from the Wikipedia article Cantellated_7-cube, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.