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:
(ñ1,ñ1,ñ3,ñ3,ñ3,ñ3)
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 IviÃÂ Weiss, Wiley-Interscience Publication, 1995, wiley.com,
- (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380âÂÂ407, MR 2,10]
- (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559âÂÂ591]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3âÂÂ45]
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
- x3x3o *b3o3o3o â thax
External links