Orthogonal projections in B6 Coxeter plane7-orthoplexRuncinated 7-orthoplexBiruncinated 7-orthoplexRuncitruncated 7-orthoplexBiruncitruncated 7-orthoplexRuncicantellated 7-orthoplexBiruncicantellated 7-orthoplexRuncicantitruncated 7-orthoplexBiruncicantitruncated 7-orthoplex
In seven-dimensional geometry, a runcinated 7-orthoplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-orthoplex.
There are 16 unique runcinations of the 7-orthoplex with permutations of truncations, and cantellations. 8 are more simply constructed from the 7-cube.
These polytopes are among 127 uniform 7-polytopes with B7 symmetry.
Runcinated 7-orthoplex Runcinated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,3{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges23520Vertices2240Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Small prismated hecatonicosaoctaexon (acronym: spaz) (Jonathan Bowers)
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Biruncinated 7-orthoplex Biruncinated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t1,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges60480Vertices6720Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Small biprismated hecatonicosaoctaexon (acronym: sibpaz) (Jonathan Bowers)Klitzing, (o3x3o3o3x3o4o - sibpaz)
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Runcitruncated 7-orthoplex Runcitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,3{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges50400Vertices6720Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Prismatotruncated hecatonicosaoctaexon (acronym: potaz) (Jonathan Bowers)Klitzing, (x3x3o3x3o3o4o - potaz)
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Biruncitruncated 7-orthoplex Biruncitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t1,2,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges120960Vertices20160Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Biprismatotruncated hecatonicosaoctaexon (acronym: baptize) (Jonathan Bowers)Klitzing, (o3x3x3o3x3o4o - baptize)
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Runcicantellated 7-orthoplex Runcicantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,2,3{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges33600Vertices6720Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Prismatorhombated hecatonicosaoctaexon (acronym: parz) (Jonathan Bowers)Klitzing, (x3o3x3x3o3o4o - parz)
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Biruncicantellated 7-orthoplex Biruncicantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t1,3,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges100800Vertices20160Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Biprismatorhombated hecatonicosoctaexon (acronym: boparz) (Jonathan Bowers)Klitzing, (o3x3o3x3x3o4o - boparz)
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Runcicantitruncated 7-orthoplex Runcicantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,2,3{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges60480Vertices13440Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Great prismated hecatonicosaoctaexon (acronym: gopaz) (Jonathan Bowers)Klitzing, (x3x3x3x3o3o4o - gopaz)
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Biruncicantitruncated 7-orthoplex Biruncicantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t1,2,3,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges161280Vertices40320Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Great biprismated hecatonicosaoctaexon (acronym: gibpaz) (Jonathan Bowers)Klitzing, (o3x3x3x3x3o4o - gibpaz)
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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) x3o3o3x3o3o4o - spaz, o3x3o3o3x3o4o - sibpaz, x3x3o3x3o3o4o - potaz, o3x3x3o3x3o4o - baptize, x3o3x3x3o3o4o - parz, o3x3o3x3x3o4o - boparz, x3x3x3x3o3o4o - gopaz, o3x3x3x3x3o4o - gibpaz
External links Polytopes of Various Dimensions Multi-dimensional Glossary