Steric 7-cubes explained
In seven-dimensional
geometry, a
stericated 7-cube (or runcinated 7-demicube) is a convex
uniform 7-polytope, being a
runcination of the uniform
7-demicube. There are 4 unique runcinations for the 7-demicube including truncation and cantellation.
Steric 7-cube
Cartesian coordinates
The Cartesian coordinates for the vertices of a steric 7-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±1,±3,±3,±3)with an odd number of plus signs.
Related polytopes
Stericantic 7-cube
Images
Steriruncic 7-cube
Images
Steriruncicantic 7-cube
Images
Related polytopes
This polytope is based on the 7-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC6 symmetry, and 32 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.
External links
