Truncated 5-demicubeCantic 5-cubeD5 Coxeter plane projectionTypeuniform 5-polytopeSchläfli symbol h2{4,3,3,3}t{3,32,1}Coxeter-Dynkin diagram = 4-faces42 total:16 r{3,3,3}16 t{3,3,3}10 t{3,3,4}Cells280 total:80 {3,3}120 t{3,3}80 {3,4}Faces640 total:480 {3}160 {6}Edges560Vertices160Vertex figure( )v{ }×{3}Coxeter groupsD5, [32,1,1]Propertiesconvex In geometry of five dimensions or higher, a cantic 5-cube, cantihalf 5-cube, truncated 5-demicube is a uniform 5-polytope, being a truncation of the 5-demicube. It has half the vertices of a cantellated 5-cube.
Cartesian coordinates The Cartesian coordinates for the 160 vertices of a cantic 5-cube centered at the origin and edge length 6 are coordinate permutations: (±1,±1,±3,±3,±3) with an odd number of plus signs.
Alternate names Cantic penteract, truncated demipenteract Truncated hemipenteract (thin) (Jonathan Bowers)
Images
Related polytopes It has half the vertices of the cantellated 5-cube, as compared here in the B5 Coxeter plane projections: Cantic 5-cubeCantellated 5-cube
This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 23 uniform 5-polytopes that can be constructed from the D5 symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.
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 *b3o3o - thin
External links
Polytopes of Various Dimensions Multi-dimensional Glossary