Cantic 6-cubeTruncated 6-demicubeD6 Coxeter plane projectionTypeuniform polypetonSchläfli symbol t0,1{3,33,1}h2{4,34}Coxeter-Dynkin diagram = 5-faces764-faces636Cells2080Faces3200Edges2160Vertices480Vertex figure( )v[{ }x{3,3}]Coxeter groupsD6, [33,1,1]Propertiesconvex
In six-dimensional geometry, a cantic 6-cube (or a truncated 6-demicube) is a uniform 6-polytope.
Alternate names Truncated 6-demicube Truncaced demihexeract Truncated hemihexeract (Acronym: thax) (Jonathan Bowers)
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.
Images
Related polytopes
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 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. x3x3o *b3o3o3o – thax
External links Polytopes of Various Dimensions Multi-dimensional Glossary