7-demicube(half 7-cube, h{4,35})Pentic 7-cubeh5{4,35}Penticantic 7-cubeh2,5{4,35}Pentiruncic 7-cubeh3,5{4,35}Pentiruncicantic 7-cubeh2,3,5{4,35}Pentisteric 7-cubeh4,5{4,35}Pentistericantic 7-cubeh2,4,5{4,35}Pentisteriruncic 7-cubeh3,4,5{4,35}Penticsteriruncicantic 7-cubeh2,3,4,5{4,35}Orthogonal projections in D7 Coxeter plane In seven-dimensional geometry, a pentic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 8 unique forms.
Pentic 7-cube Pentic 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,4{3,34,1}h5{4,35}Coxeter-Dynkin diagram6-faces5-faces4-facesCellsFacesEdges13440Vertices1344Vertex figureCoxeter groupsD7, [34,1,1]Propertiesconvex
Alternate names Small cellated demihepteract (acronym: sochesa)Klitzing, (x3o3o *b3o3o3x3o - sochesa)
Cartesian coordinates The Cartesian coordinates for the vertices of a pentic 7-cube centered at the origin are coordinate permutations: (±1,±1,±1,±1,±1,±3,±3) with an odd number of plus signs.
Images
Related polytopes
Penticantic 7-cube
Alternate names Cellitruncated demihepteract (acronym: cothesa)Klitzing, (x3x3o *b3o3o3x3o - cothesa)
Images
Pentiruncic 7-cube
Alternate names Cellirhombated demihepteract (acronym: crohesa)Klitzing, (x3o3o *b3x3o3x3o - crohesa)
Images
Pentiruncicantic 7-cube
Alternate names Celligreatorhombated demihepteract (acronym: cagrohesa)Klitzing, (x3x3o *b3x3o3x3o - cagrohesa)
Images
Pentisteric 7-cube
Alternate names Celliprismated demihepteract (acronym: caphesa)Klitzing, (x3o3o *b3o3x3x3o - caphesa)
Images
Pentistericantic 7-cube
Alternate names Celliprismatotruncated demihepteract (acronym: capthesa)Klitzing, (x3x3o *b3o3x3x3o - capthesa)
Images
Pentisteriruncic 7-cube
Alternate names Celliprismatorhombated demihepteract (acronym: coprahesa)Klitzing, (x3o3o *b3x3x3x3o - coprahesa)
Images
Pentisteriruncicantic 7-cube
Alternate names Great cellated demihepteract (acronym: gochesa)Klitzing, (x3x3o *b3x3x3x3o - gochesa)
Images
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 BC7 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