6-demicube = Steric 6-cube = Stericantic 6-cube = Steriruncic 6-cube = Steriruncicantic 6-cube = Orthogonal projections in D5 Coxeter plane In six-dimensional geometry, a steric 6-cube is a convex uniform 6-polytope. There are unique 4 steric forms of the 6-cube.
Steric 6-cube Steric 6-cubeTypeuniform 6-polytopeSchläfli symbol t0,3{3,33,1}h4{4,34}Coxeter-Dynkin diagram = 5-faces4-facesCellsFacesEdges3360Vertices480Vertex figureCoxeter groupsD6, [33,1,1]Propertiesconvex
Alternate names Runcinated demihexeract Runcinated 6-demicube Small prismated hemihexeract (Acronym: sophax) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 480 vertices of a steric 6-cube centered at the origin are coordinate permutations: (±1,±1,±1,±1,±1,±3) with an odd number of plus signs.
Images
Related polytopes
Stericantic 6-cube Stericantic 6-cubeTypeuniform 6-polytopeSchläfli symbol t0,1,3{3,33,1}h2,4{4,34}Coxeter-Dynkin diagram = 5-faces4-facesCellsFacesEdges12960Vertices2880Vertex figureCoxeter groupsD6, [33,1,1]Propertiesconvex
Alternate names Runcitruncated demihexeract Runcitruncated 6-demicube Prismatotruncated hemihexeract (Acronym: pithax) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 2880 vertices of a stericantic 6-cube centered at the origin are coordinate permutations: (±1,±1,±1,±3,±3,±5) with an odd number of plus signs.
Images
Steriruncic 6-cube Steriruncic 6-cubeTypeuniform 6-polytopeSchläfli symbol t0,2,3{3,33,1}h3,4{4,34}Coxeter-Dynkin diagram = 5-faces4-facesCellsFacesEdges7680Vertices1920Vertex figureCoxeter groupsD6, [33,1,1]Propertiesconvex
Alternate names Runcicantellated demihexeract Runcicantellated 6-demicube Prismatorhombated hemihexeract (Acronym: prohax) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 1920 vertices of a steriruncic 6-cube centered at the origin are coordinate permutations: (±1,±1,±1,±1,±3,±5) with an odd number of plus signs.
Images
Steriruncicantic 6-cube Steriruncicantic 6-cubeTypeuniform 6-polytopeSchläfli symbol t0,1,2,3{3,32,1}h2,3,4{4,34}Coxeter-Dynkin diagram = 5-faces4-facesCellsFacesEdges17280Vertices5760Vertex figureCoxeter groupsD6, [33,1,1]Propertiesconvex
Alternate names Runcicantitruncated demihexeract Runcicantitruncated 6-demicube Great prismated hemihexeract (Acronym: gophax) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 5760 vertices of a steriruncicantic 6-cube centered at the origin are coordinate permutations: (±1,±1,±1,±3,±5,±7) 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. x3o3o *b3o3x3o - sophax, x3x3o *b3o3x3o - pithax, x3o3o *b3x3x3o - prohax, x3x3o *b3x3x3o - gophax
External links
Polytopes of Various Dimensions Multi-dimensional Glossary