7-orthoplexCantellated 7-orthoplexBicantellated 7-orthoplexBirectified 7-orthoplexCantitruncated 7-orthoplexBicantitruncated 7-orthoplexCantellated 7-cubeBicantellated 7-cubeTricantellated 7-cubeCantitruncated 7-cubeBicantitruncated 7-cubeTricantitruncated 7-cubeOrthogonal projections in B6 Coxeter plane
In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex.
There are ten degrees of cantellation for the 7-orthoplex, including truncations. Six are most simply constructible from the dual 7-cube.
Cantellated 7-orthoplex Cantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol rr{3,3,3,3,3,4}Coxeter-Dynkin diagram6-faces5-faces4-facesCellsFacesEdges7560Vertices840Vertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Small rhombated hecatonicosaoctaexon (acronym: sarz) (Jonathan Bowers)
Images
Bicantellated 7-orthoplex Bicantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol 2rr{3,3,3,3,3,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Small birhombated hecatonicosaoctaexon (acronym: sebraz) (Jonathan Bowers)Klitzing, (o3x3o3x3o3o4o - sebraz)
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Cantitruncated 7-orthoplex Cantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol tr{3,3,3,3,3,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges8400Vertices1680Vertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Great rhombated hecatonicosaoctaexon (acronym: garz) (Jonathan Bowers)Klitzing, (x3x3x3o3o3o4o - garz)
Images
Bicantitruncated 7-orthoplex Bicantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol 2tr{3,3,3,3,3,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges30240Vertices6720Vertex figureCoxeter groupsB7, [4,3,3,3,3,3]Propertiesconvex
Alternate names Great birhombated hecatonicosoctaexon (acronym: gebraz) (Jonathan Bowers)Klitzing, (o3x3x3x3o3o4o - gebraz)
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. 1966 x3o3x3o3o3o4o - sarz, o3x3o3x3o3o4o - sebraz, x3x3x3o3o3o4o - garz, o3x3x3x3o3o4o - gebraz
External links Polytopes of Various Dimensions Multi-dimensional Glossary