Orthogonal projections in B6 Coxeter plane7-cubeStericated 7-cubeBistericated 7-cubeSteritruncated 7-cubeBisteritruncated 7-cubeStericantellated 7-cubeBistericantellated 7-cubeStericantitruncated 7-cubeBistericantitruncated 7-cubeSteriruncinated 7-cubeSteriruncitruncated 7-cubeSteriruncicantellated 7-cubeBisteriruncitruncated 7-cubeSteriruncicantitruncated 7-cubeBisteriruncicantitruncated 7-cube In seven-dimensional geometry, a stericated 7-cube is a convex uniform 7-polytope with 4th-order truncations (sterication) of the regular 7-cube.
There are 24 unique sterication for the 7-cube with permutations of truncations, cantellations, and runcinations. 10 are more simply constructed from the 7-orthoplex. This polytope is one of 127 uniform 7-polytopes with B7 symmetry.
Stericated 7-cube Stericated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Small cellated hepteract (acronym: scosa) (Jonathan Bowers)Klitzing, (x4o3o3o3x3o3o - scosa)
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Bistericated 7-cube Bistericated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Small bicellated hepteractihecatonicosaoctaexon (acronym: sabcosaz) (Jonathan Bowers)Klitzing, (o4x3o3o3o3x3o - sabcosaz)
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Steritruncated 7-cube Steritruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Cellitruncated hepteract (acronym: catsa) (Jonathan Bowers)Klitzing, (x4x3o3o3x3o3o - catsa)
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Bisteritruncated 7-cube Bisteritruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,2,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bicellitruncated hepteract (acronym: bactasa) (Jonathan Bowers)Klitzing, (o4x3x3o3o3x3o - bactasa)
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Stericantellated 7-cube Stericantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,2,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Cellirhombated hepteract (acronym: carsa) (Jonathan Bowers)Klitzing, (x4o3x3o3x3o3o - carsa)
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Bistericantellated 7-cube Bistericantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,3,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bicellirhombihepteract (acronym: bacresaz) (Jonathan Bowers)Klitzing, (o4x3o3x3o3x3o - bacresaz)
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Stericantitruncated 7-cube Stericantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,2,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Celligreatorhombated hepteract (acronym: cogarsa) (Jonathan Bowers)Klitzing, (x4x3x3o3x3o3o - cogarsa)
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Bistericantitruncated 7-cube Bistericantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,2,3,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bicelligreatorhombated hepteract (acronym: becgresa) (Jonathan Bowers)Klitzing, (o4x3x3x3o3x3o - becgresa)
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Steriruncinated 7-cube Steriruncinated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,3,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Celliprismated hepteract (acronym: capsa) (Jonathan Bowers)Klitzing, (x4o3o3x3x3o3o - capsa)
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Steriruncitruncated 7-cube Steriruncitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,3,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Celliprismatotruncated hepteract (acronym: captesa) (Jonathan Bowers)Klitzing, (x4x3o3x3x3o3o - captesa)
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Steriruncicantellated 7-cube Steriruncicantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,2,3,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Celliprismatorhombated hepteract (acronym: copresa) (Jonathan Bowers)Klitzing, (x4o3x3x3x3o3o - copresa)
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Bisteriruncitruncated 7-cube Bisteriruncitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,2,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bicelliprismatotruncated hepteractihecatonicosaoctaexon (acronym: bocaptosaz) (Jonathan Bowers)Klitzing, (o4x3x3o3x3x3o - bocaptosaz)
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Steriruncicantitruncated 7-cube Steriruncicantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,2,3,4{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Great cellated hepteract (acronym: gacosa) (Jonathan Bowers)Klitzing, (x4x3x3x3x3o3o - gacosa)
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Bisteriruncicantitruncated 7-cube
Bisteriruncicantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t1,2,3,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Great bicellated hepteractihecatonicosaoctaexon (acronym: gabcosaz) (Jonathan Bowers) Klitzing, (o4x3x3x3x3x3o - gabcosaz)
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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.
External links Polytopes of Various Dimensions Multi-dimensional Glossary