5-cubeRuncic 5-cube = 5-demicube = Runcicantic 5-cube = Orthogonal projections in B5 Coxeter plane In five-dimensional geometry, a runcic 5-cube, runcic 5-demicube or runcihalf 5-cube, is a convex uniform 5-polytope. There are 2 runcic forms for the 5-cube. Runcic 5-cubes have half the vertices of runcinated 5-cubes.
Runcic 5-cube Runcic 5-cubeTypeuniform 5-polytopeSchläfli symbol h3{4,3,3,3}Coxeter-Dynkin diagram4-faces42Cells360Faces880Edges720Vertices160Vertex figureCoxeter groupsD5, [32,1,1]Propertiesconvex
Alternate names Cantellated 5-demicube/demipenteract Small rhombated hemipenteract (sirhin) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 960 vertices of a runcic 5-cubes centered at the origin are coordinate permutations: (±1,±1,±1,±3,±3) with an odd number of plus signs.
Images
Related polytopes It has half the vertices of the runcinated 5-cube, as compared here in the B5 Coxeter plane projections: Runcic 5-cubeRuncinated 5-cube
Runcicantic 5-cube Runcicantic 5-cubeTypeuniform 5-polytopeSchläfli symbol t0,1,2{3,32,1}h2,3{4,33}Coxeter-Dynkin diagram4-faces42Cells360Faces1040Edges1200Vertices480Vertex figureCoxeter groupsD5, [32,1,1]Propertiesconvex
Alternate names Cantitruncated 5-demicube/demipenteract Great rhombated hemipenteract (girhin) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 480 vertices of a runcicantic 5-cube centered at the origin are coordinate permutations: (±1,±1,±3,±5,±5) with an odd number of plus signs.
Images
Related polytopes It has half the vertices of the runcicantellated 5-cube, as compared here in the B5 Coxeter plane projections: Runcicantic 5-cubeRuncicantellated 5-cube
Related polytopes These polytopes are based on the 5-demicube, a member 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. x3o3o *b3x3o - sirhin, x3x3o *b3x3o - girhin
External links
Polytopes of Various Dimensions Multi-dimensional Glossary