7-demicubeSteric 7-cubeStericantic 7-cubeSteriruncic 7-cubeSteriruncicantic 7-cubeOrthogonal projections in D7 Coxeter plane 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 Steric 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,3{3,34,1}h4{4,35}Coxeter-Dynkin diagram6-faces5-faces4-facesCellsFacesEdges20160Vertices2240Vertex figureCoxeter groupsD7, [34,1,1]Propertiesconvex
Alternate names Small prismated demihepteract (acronym: sphosa)Klitzing, (x3o3o *b3o3x3o3o - sphosa)
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.
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Related polytopes
Stericantic 7-cube
Alternate names Prismatotruncated demihepteract (acronym: pothesa)Klitzing, (x3x3o *b3o3x3o3o - pothesa)
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Steriruncic 7-cube
Alternate names Prismatorhombated demihepteract (acronym: prohesa)Klitzing, (x3o3o *b3x3x3o3o - prohesa)
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Steriruncicantic 7-cube
Alternate names Great prismated demihepteract (acronym: gephosa)Klitzing, (x3x3o *b3x3x3o3o - gephosa)
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Related polytopes These polytopes are based on the 7-demicube, a member 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:
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 Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com, (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
Polytopes of Various Dimensions Multi-dimensional Glossary