7-cubeRuncinated 7-cubeBiruncinated 7-cubeRuncitruncated 7-cubeBiruncitruncated 7-cubeRuncicantellated 7-cubeBiruncicantellated 7-cubeRuncicantitruncated 7-cubeBiruncicantitruncated 7-cubeOrthogonal projections in B6 Coxeter plane
In seven-dimensional geometry, a runcinated 7-cube is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-cube.
There are 16 unique runcinations of the 7-cube with permutations of truncations, and cantellations. 8 are more simply constructed from the 7-orthoplex.
These polytopes are among 127 uniform 7-polytopes with B7 symmetry.
Runcinated 7-cube Runcinated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,3{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges33600Vertices4480Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Small prismated hepteract (acronym: spesa) (Jonathan Bowers)Klitzing, (x4o3o3x3o3o3o - spesa)
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Biruncinated 7-cube Biruncinated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges67200Vertices8960Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Small biprismated hepteract (Acronym sibposa) (Jonathan Bowers)Klitzing, (o4x3o3o3x3o3o - sibposa)
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Runcitruncated 7-cube Runcitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,3{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges73920Vertices13440Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Prismatotruncated hepteract (acronym: petsa) (Jonathan Bowers)Klitzing, (x4x3o3x3o3o3o - petsa)
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Biruncitruncated 7-cube Biruncitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,2,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges134400Vertices26880Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Biprismatotruncated hepteract (acronym: biptesa) (Jonathan Bowers)Klitzing, (o4x3x3o3x3o3o - biptesa)
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Runcicantellated 7-cube Runcicantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,2,3{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges53760Vertices13440Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Prismatorhombated hepteract (acronym: parsa) (Jonathan Bowers)Klitzing, (x4o3x3x3o3o3o - parsa)
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Biruncicantellated 7-cube Biruncicantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,3,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges120960Vertices26880Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Biprismatorhombated hepteract (acronym: bopresa) (Jonathan Bowers)Klitzing, (o4x3o3x3x3o3o - bopresa)
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Runcicantitruncated 7-cube Runcicantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,2,3{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges94080Vertices26880Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Great prismated hepteract (acronym: gapsa) (Jonathan Bowers)Klitzing, (x4x3x3x3o3o3o - gapsa)
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Biruncicantitruncated 7-cube Biruncicantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,2,3,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges188160Vertices53760Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Great biprismated hepteract (acronym: gibposa) (Jonathan Bowers)Klitzing, (o4x3x3x3x3o3o - gibposa)
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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. (1966) x4o3o3x3o3o3o - spesa, o4x3o3o3x3o3o - sibposa, x4x3o3x3o3o3o - petsa, o4x3x3o3x3o3o - biptesa, x4o3x3x3o3o3o - parsa, o4x3o3x3x3o3o - bopresa, x4x3x3x3o3o3o - gapsa, o4x3x3x3x3o3o - gibposa
External links Polytopes of Various Dimensions Multi-dimensional Glossary