In seven-dimensional geometry, a hexic 7-cube is a convex uniform 7-polytope, constructed from the uniform 7-demicube. There are 16 unique forms.
Hexic 7-cube
Cartesian coordinates
The Cartesian coordinates for the vertices of a hexic 7-cube centered at the origin are coordinate permutations:
(ñ1,ñ1,ñ1,ñ1,ñ1,ñ1,ñ3)
with an odd number of plus signs.
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Hexicantic 7-cube
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Hexiruncic 7-cube
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Hexisteric 7-cube
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Hexipentic 7-cube
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Hexiruncicantic 7-cube
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Hexistericantic 7-cube
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Hexipenticantic 7-cube
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Hexisteriruncic 7-cube
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Hexipentiruncic 7-cube
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Hexipentisteric 7-cube
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Hexisteriruncicantic 7-cube
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Hexipentiruncicantic 7-cube
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Hexipentisteriruncic 7-cube
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Hexipentistericantic 7-cube
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Hexipentisteriruncicantic 7-cube
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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 D<sub>7</sub> symmetry, 63 are shared by the BC<sub>7</sub> symmetry, and 32 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 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