Orthogonal projections in B6 Coxeter plane7-orthoplexStericated 7-orthoplexSteritruncated 7-orthoplexBisteritruncated 7-orthoplexStericantellated 7-orthoplexStericantitruncated 7-orthoplexBistericantitruncated 7-orthoplexSteriruncinated 7-orthoplexSteriruncitruncated 7-orthoplexSteriruncicantellated 7-orthoplexSteriruncicantitruncated 7-orthoplex In seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex.
There are 24 unique sterication for the 7-orthoplex with permutations of truncations, cantellations, and runcinations. 14 are more simply constructed from the 7-cube. This polytope is one of 127 uniform 7-polytopes with B7 symmetry.
Stericated 7-orthoplex Stericated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Small cellated hecatonicosaoctaexon (acronym: scaz) (Jonathan Bowers)Klitzing, (x3o3o3o3x3o4o - scaz)
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Steritruncated 7-orthoplex Steritruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Cellitruncated hecatonicosaoctaexon (acronym: catz) (Jonathan Bowers)Klitzing, (x3x3o3o3x3o4o - catz)
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Bisteritruncated 7-orthoplex Bisteritruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t1,2,5{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bicellitruncated hecatonicosaoctaexon (acronym: boctaz) (Jonathan Bowers)Klitzing, (o3x3x3o3o3x4o - boctaz)
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Stericantellated 7-orthoplex Stericantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,2,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Cellirhombated hecatonicosaoctaexon (acronym: craze) (Jonathan Bowers)Klitzing, (x3o3x3o3x3o4o - craze)
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Stericantitruncated 7-orthoplex Stericantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,2,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Celligreatorhombated hecatonicosaoctaexon (acronym: cogarz) (Jonathan Bowers)Klitzing, (x3x3x3o3x3o4o - cogarz)
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Bistericantitruncated 7-orthoplex Bistericantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t1,2,3,5{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bicelligreatorhombated hecatonicosaoctaexon (acronym: becogarz) (Jonathan Bowers)Klitzing, (o3x3x3x3o3x4o - becogarz)
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Steriruncinated 7-orthoplex Steriruncinated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,3,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Celliprismated hecatonicosaoctaexon (acronym: copaz) (Jonathan Bowers)Klitzing, (x3o3o3x3x3o4o - copaz)
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Steriruncitruncated 7-orthoplex Steriruncitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,3,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Celliprismatotruncated hecatonicosaoctaexon (acronym: captaz) (Jonathan Bowers)Klitzing, (x3x3o3x3x3o4o - captaz)
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Steriruncicantellated 7-orthoplex Steriruncicantellated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,2,3,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Celliprismatorhombated hecatonicosaoctaexon (acronym: caparz) (Jonathan Bowers)Klitzing, (x3o3x3x3x3o4o - caparz)
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Steriruncicantitruncated 7-orthoplex Steriruncicantitruncated 7-orthoplexTypeuniform 7-polytopeSchläfli symbol t0,1,2,3,4{35,4}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Great cellated hecatonicosaoctaexon (acronym: gocaz) (Jonathan Bowers)Klitzing, (x3x3x3x3x3o4o - gocaz)
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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. x3o3o3o3x3o4o - scaz, x3x3o3o3x3o4o - catz, o3x3x3o3o3x4o - boctaz, x3o3x3o3x3o4o - craze, x3x3x3o3x3o4o - cogarz, o3x3x3x3o3x4o - becogarz, x3o3o3x3x3o4o - copaz, x3x3o3x3x3o4o - captaz, x3o3x3x3x3o4o - caparz, x3x3x3x3x3o4o - gocaz
External links Polytopes of Various Dimensions Multi-dimensional Glossary