Orthogonal projections in B6 Coxeter plane7-orthoplexPentellated 7-orthoplexPentitruncated 7-orthoplexPenticantellated 7-orthoplex Penticantitruncated 7-orthoplex Pentiruncinated 7-orthoplex Pentiruncitruncated 7-orthoplex Pentiruncicantellated 7-orthoplex Pentiruncicantitruncated 7-orthoplex Pentistericated 7-orthoplex Pentisteritruncated 7-orthoplexPentistericantellated 7-orthoplex Pentistericantitruncated 7-orthoplex Pentisteriruncinated 7-orthoplex Pentisteriruncitruncated 7-orthoplex Pentisteriruncicantellated 7-orthoplex Pentisteriruncicantitruncated 7-orthoplex In seven-dimensional geometry, a pentellated 7-orthoplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-orthoplex.
There are 32 unique of the 7-orthoplex with permutations of truncations, cantellations, runcinations, and . 16 are more simply constructed relative to the 7-cube.
These polytopes are a part of a set of 127 uniform 7-polytopes with B7 symmetry.
Pentellated 7-orthoplex Pentellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges20160Vertices2688Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Small hecatonicosaoctaexon (acronym: Staz) (Jonathan Bowers)Klitzing, (x3o3o3o3o3x4o - staz)
Coordinates Coordinates are permutations of (0,1,1,1,1,1,2)
Images
Pentitruncated 7-orthoplex Pentitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges87360Vertices13440 Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Teritruncated hecatonicosaoctaexon (acronym: Tetaz) (Jonathan Bowers)Klitzing, (x3x3o3o3o3x4o - tetaz)
Images
Coordinates Coordinates are permutations of (0,1,1,1,1,2,3).
Penticantellated 7-orthoplex Penticantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,2,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges188160Vertices26880 Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Terirhombated hecatonicosaoctaexon (acronym: Teroz) (Jonathan Bowers)Klitzing, (x3o3x3o3o3x4o - teroz)
Coordinates Coordinates are permutations of (0,1,1,1,2,2,3).
Images
Penticantitruncated 7-orthoplex Penticantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,2,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges295680Vertices53760Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Terigreatorhombated hecatonicosaoctaexon (acronym: Tograz) (Jonathan Bowers)Klitzing, (x3x3x3oxo3x4o - tograz)
Coordinates Coordinates are permutations of (0,1,1,1,2,3,4).
Images
Pentiruncinated 7-orthoplex Pentiruncinated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,3,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges174720Vertices26880Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Teriprismated hecatonicosaoctaexon (acronym: Topaz) (Jonathan Bowers)Klitzing, (x3o3o3x3o3x4o - topaz)
Coordinates The coordinates are permutations of (0,1,1,2,2,2,3).
Images
Pentiruncitruncated 7-orthoplex
Pentiruncitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,3,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges443520Vertices80640 Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Teriprismatotruncated hecatonicosaoctaexon (acronym: Toptaz) (Jonathan Bowers)Klitzing, (x3x3o3x3o3x4o - toptaz)
Coordinates Coordinates are permutations of (0,1,1,2,2,3,4).
Images
Pentiruncicantellated 7-orthoplex Pentiruncicantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,2,3,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges403200Vertices80640Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Teriprismatorhombated hecatonicosaoctaexon (acronym: Toparz) (Jonathan Bowers)Klitzing, (x3o3x3x3o3x4o - toparz)
Coordinates Coordinates are permutations of (0,1,1,2,3,3,4).
Images
Pentiruncicantitruncated 7-orthoplex Pentiruncicantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,2,3,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges725760Vertices161280Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Terigreatoprismated hecatonicosaoctaexon (acronym: Tegopaz) (Jonathan Bowers)Klitzing, (x3x3x3x3o3x4o - tegopaz)
Coordinates Coordinates are permutations of (0,1,1,2,3,4,5).
Images
Pentistericated 7-orthoplex Pentistericated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,4,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges67200Vertices13440Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericellated hecatonicosaoctaexon (acronym: Tocaz) (Jonathan Bowers)Klitzing, (x3o3o3o3x3x4o - tocaz)
Images
Coordinates Coordinates are permutations of (0,1,2,2,2,2,3).
Pentisteritruncated 7-orthoplex Pentisteritruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,4,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges241920Vertices53760Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericellitruncated hecatonicosaoctaexon (acronym: Tacotaz) (Jonathan Bowers)Klitzing, (x3x3o3o3x3x4o - tacotaz)
Coordinates Coordinates are permutations of (0,1,2,2,2,3,4).
Images
Pentistericantellated 7-orthoplex Pentistericantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,2,4,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges403200Vertices80640Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericellirhombated hecatonicosaoctaexon (acronym: Tocarz) (Jonathan Bowers)Klitzing, (x3o3x3o3x3x4o - tocarz)
Coordinates Coordinates are permutations of (0,1,2,2,3,3,4).
Images
Pentistericantitruncated 7-orthoplex Pentistericantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,2,4,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges645120Vertices161280Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericelligreatorhombated hecatonicosaoctaexon (acronym: Tecagraz) (Jonathan Bowers)Klitzing, (x3x3x3o3x3x4o - tecagraz)
Coordinates Coordinates are permutations of (0,1,2,2,3,4,5).
Images
Pentisteriruncinated 7-orthoplex Pentisteriruncinated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,3,4,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges241920Vertices53760Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bipenticantitruncated 7-orthoplex as t1,2,3,6{35,4} Tericelliprismated hecatonicosaoctaexon (acronym: Tecpaz) (Jonathan Bowers)Klitzing, (x3o3o3x3x3x4o - tecpaz)
Coordinates Coordinates are permutations of (0,1,2,3,3,3,4).
Images
Pentisteriruncitruncated 7-orthoplex Pentisteriruncitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,3,4,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges645120Vertices161280Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericelliprismatotruncated hecatonicosaoctaexon (acronym: Tecpotaz) (Jonathan Bowers)Klitzing, (x3x3o3x3x3x4o - tecpotaz)
Coordinates Coordinates are permutations of (0,1,2,3,3,4,5).
Images
Pentisteriruncicantellated 7-orthoplex Pentisteriruncicantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,2,3,4,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges645120 Vertices161280Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bipentiruncicantitruncated 7-orthoplex as t1,2,3,4,6{35,4} Tericelliprismatorhombated hecatonicosaoctaexon (acronym: Tacparez) (Jonathan Bowers)Klitzing, (x3o3x3x3x3x4o - tacparez)
Coordinates Coordinates are permutations of (0,1,2,3,4,4,5).
Images
Pentisteriruncicantitruncated 7-orthoplex Pentisteriruncicantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,2,3,4,5{35,4}Coxeter diagram6-faces5-faces4-facesCellsFacesEdges1128960Vertices322560Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Great hecatonicosaoctaexon (acronym: Gotaz) (Jonathan Bowers)Klitzing, (x3x3x3x3x3x4o - gotaz)
Coordinates Coordinates are permutations of (0,1,2,3,4,5,6).
Images
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. x3o3o3o3o3x4o - staz, x3x3o3o3o3x4o - tetaz, x3o3x3o3o3x4o - teroz, x3x3x3oxo3x4o - tograz, x3o3o3x3o3x4o - topaz, x3x3o3x3o3x4o - toptaz, x3o3x3x3o3x4o - toparz, x3x3x3x3o3x4o - tegopaz, x3o3o3o3x3x4o - tocaz, x3x3o3o3x3x4o - tacotaz, x3o3x3o3x3x4o - tocarz, x3x3x3o3x3x4o - tecagraz, x3o3o3x3x3x4o - tecpaz, x3x3o3x3x3x4o - tecpotaz, x3o3x3x3x3x4o - tacparez, x3x3x3x3x3x4o - gotaz
External links Polytopes of Various Dimensions Multi-dimensional Glossary