Cantic 6-cube explained
| bgcolor=#e7dcc3 colspan=2 | Cantic 6-cube
Truncated 6-demicube |
|---|
| bgcolor=#ffffff align=center colspan=2 |
D6 Coxeter plane projection |
| Type | uniform polypeton |
| Schläfli symbol | t0,1
h2 |
| Coxeter-Dynkin diagram | = |
| 5-faces | 76 |
| 4-faces | 636 |
| Cells | 2080 |
| Faces | 3200 |
| Edges | 2160 |
| Vertices | 480 |
| Vertex figure | v[{ }x{3,3}] |
| Coxeter groups | D6, [3<sup>3,1,1</sup>] |
| Properties | convex | |
In six-dimensional geometry, a cantic 6-cube (or a truncated 6-demicube) is a uniform 6-polytope.
Alternate names
- Truncated 6-demicube/demihexeract (Acronym thax) (Jonathan Bowers)[1]
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.
Related polytopes
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:
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.
- x3x3o *b3o3o3o – thax
External links
Notes and References
- Klitizing, (x3x3o *b3o3o3o – thax)
