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Cantic 6-cube

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

Related polytopes

There are 47 uniform polytopes with D<sub>6</sub> symmetry, 31 are shared by the B<sub>6</sub> symmetry, and 16 are unique:

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 Ivić 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

External links