In six-dimensional geometry, a cantellated 6-cube is a convex uniform 6-polytope, being a cantellation of the regular 6-cube.
There are 8 cantellations for the 6-cube, including truncations. Half of them are more easily constructed from the dual 6-orthoplex.
Cantellated 6-cube
Alternate names
- Cantellated hexeract
- Small rhombated hexeract (acronym: srox) (Jonathan Bowers)
Images
Bicantellated 6-cube
Alternate names
- Bicantellated hexeract
- Small birhombated hexeract (acronym: saborx) (Jonathan Bowers)
Images
Cantitruncated 6-cube
Alternate names
- Cantitruncated hexeract
- Great rhombihexeract (acronym: grox) (Jonathan Bowers)
Images
It is fourth in a series of cantitruncated hypercubes:
Bicantitruncated 6-cube
Alternate names
- Bicantitruncated hexeract
- Great birhombihexeract (acronym: gaborx) (Jonathan Bowers)
Images
Related polytopes
These polytopes are part of a set of 63 uniform 6-polytopes generated from the B<sub>6</sub> Coxeter plane, including the regular 6-cube and 6-orthoplex.
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.
- o3o3o3x3o4x - srox, o3o3x3o3x4o - saborx, o3o3o3x3x4x - grox, o3o3x3x3x4o - gaborx
External links