7-cubeCantellated 7-cubeBicantellated 7-cubeTricantellated 7-cubeBirectified 7-cubeCantitruncated 7-cubeBicantitruncated 7-cubeTricantitruncated 7-cubeCantellated 7-orthoplexBicantellated 7-orthoplexCantitruncated 7-orthoplexBicantitruncated 7-orthoplexOrthogonal projections in B6 Coxeter plane
In seven-dimensional geometry, a cantellated 7-cube is a convex uniform 7-polytope, being a cantellation of the regular 7-cube.
There are 10 degrees of cantellation for the 7-cube, including truncations. 4 are most simply constructible from the dual 7-orthoplex.
Cantellated 7-cube Cantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol rr{4,3,3,3,3,3}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges16128Vertices2688Vertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Small rhombated hepteract (acronym: sersa) (Jonathan Bowers)
Images
Bicantellated 7-cube Bicantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol r2r{4,3,3,3,3,3}Coxeter diagrams6-faces5-faces4-facesCellsFacesEdges40320Vertices6720Vertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Small birhombated hepteract (acronym: sibrosa) (Jonathan Bowers)Klitzing, (o4x3o3x3o3o3o - sibrosa)
Images
Tricantellated 7-cube Tricantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol r3r{4,3,3,3,3,3}Coxeter diagrams6-faces5-faces4-facesCellsFacesEdges47040Vertices6720Vertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Small trirhombihepteractihecatonicosaoctaexon (acronym: strasaz) (Jonathan Bowers)Klitzing, (o4o3x3o3x3o3o - strasaz)
Images
Cantitruncated 7-cube Cantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol tr{4,3,3,3,3,3}Coxeter diagrams6-faces5-faces4-facesCellsFacesEdges18816Vertices5376Vertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Great rhombated hepteract (acronym: gersa) (Jonathan Bowers)Klitzing, (x4x3x3o3o3o3o - gersa)
Images
It is fifth in a series of cantitruncated hypercubes:
Bicantitruncated 7-cube Bicantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol r2r{4,3,3,3,3,3}Coxeter diagrams6-faces5-faces4-facesCellsFacesEdges47040Vertices13440Vertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Great birhombated hepteract (acronym: gibrosa) (Jonathan Bowers)Klitzing, (o4x3x3x3o3o3o - gibrosa)
Images
Tricantitruncated 7-cube Tricantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t3r{4,3,3,3,3,3}Coxeter diagrams6-faces5-faces4-facesCellsFacesEdges53760Vertices13440Vertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Great trirhombihepteractihecatonicosaoctaexon (acronym: gotrasaz) (Jonathan Bowers)Klitzing, (o4o3x3x3x3o3o - gotrasaz)
Images
Related polytopes These polytopes are from a family of 127 uniform 7-polytopes with B7 symmetry.
See also List of B7 polytopes
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. x4o3x3o3o3o3o - sersa, o4x3o3x3o3o3o - sibrosa, o4o3x3o3x3o3o - strasaz, x4x3x3o3o3o3o - gersa, o4x3x3x3o3o3o - gibrosa, o4o3x3x3x3o3o - gotrasaz
External links Polytopes of Various Dimensions Multi-dimensional Glossary