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Cantic 6-cube

Shape in six-dimensional geometry

Shape in six-dimensional geometry

Cantic 6-cubeTruncated 6-demicube
[[File:Truncated 6-demicube D6.svg280px]]D6 Coxeter plane projection
Type
Schläfli symbol
Coxeter-Dynkin diagram
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

In six-dimensional geometry, a cantic 6-cube (or a truncated 6-demicube) is a uniform 6-polytope.

Alternate names

  • Truncated 6-demicube
  • Truncaced demihexeract
  • Truncated hemihexeract (Acronym: thax) (Jonathan Bowers)

Cartesian coordinates

The Cartesian coordinates for the 480 vertices of a cantic 6-cube centered at the origin and edge length 6 are coordinate permutations: : (±1,±1,±3,±3,±3,±3) with an odd number of plus signs.

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.
  • x3x3o *b3o3o3o – thax
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