In seven-dimensional geometry, a pentellated 7-cube is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-cube. There are 32 unique of the 7-cube with permutations of truncations, cantellations, runcinations, and . 16 are more simply constructed relative to the 7-orthoplex.
7-cubePentellated 7-cubePentitruncated 7-cubePenticantellated 7-cubePenticantitruncated 7-cubePentiruncinated 7-cubePentiruncitruncated 7-cubePentiruncicantellated 7-cubePentiruncicantitruncated 7-cubePentistericated 7-cubePentisteritruncated 7-cubePentistericantellated 7-cubePentistericantitruncated 7-cubePentisteriruncinated 7-cubePentisteriruncitruncated 7-cubePentisteriruncicantellated 7-cubePentisteriruncicantitruncated 7-cube
Pentellated 7-cube Pentellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Small hepteract (acronym: stesa) (Jonathan Bowers)
Images
Pentitruncated 7-cube Pentitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Teritruncated hepteract (acronym: tetsa) (Jonathan Bowers)Klitzing, (x4x3o3o3o3x3o - tetsa)
Images
Penticantellated 7-cube Penticantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,2,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Terirhombated hepteract (acronym: tersa) (Jonathan Bowers)Klitzing, (x4o3x3o3o3x3o - tersa)
Images
Penticantitruncated 7-cube Penticantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,2,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Terigreatorhombated hepteract (acronym: togresa) (Jonathan Bowers)Klitzing, (x4x3x3o3o3x3o - togresa)
Images
Pentiruncinated 7-cube Pentiruncinated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,3,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Teriprismated hepteract (acronym: tapsa) (Jonathan Bowers)Klitzing, (x4o3o3x3o3x3o - tapsa)
Images
Pentiruncitruncated 7-cube Pentiruncitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,3,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Teriprismatotruncated hepteract (acronym: toptosa) (Jonathan Bowers)Klitzing, (x4x3o3x3o3x3o - toptosa)
Images
Pentiruncicantellated 7-cube Pentiruncicantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,2,3,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Teriprismatorhombated hepteract (acronym: topresa) (Jonathan Bowers)Klitzing, (x4o3x3x3o3x3o - topresa)
Images
Pentiruncicantitruncated 7-cube Pentiruncicantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,2,3,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Terigreatoprismated hepteract (acronym: togapsa) (Jonathan Bowers)Klitzing, (x4x3x3x3o3x3o - togapsa)
Images
Pentistericated 7-cube Pentistericated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericellated hepteract (acronym: tacosa) (Jonathan Bowers)Klitzing, (x4o3o3o3x3x3o - tacosa)
Images
Pentisteritruncated 7-cube Pentisteritruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericellitruncated hepteract (acronym: tecatsa) (Jonathan Bowers)Klitzing, (x4x3o3o3x3x3o - tecatsa)
Images
Pentistericantellated 7-cube Pentistericantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,2,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericellirhombated hepteract (acronym: tecresa) (Jonathan Bowers)Klitzing, (x4o3x3o3x3x3o - tecresa)
Images
Pentistericantitruncated 7-cube Pentistericantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,2,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericelligreatorhombated hepteract (acronym: tecgresa) (Jonathan Bowers)Klitzing, (x4x3x3o3x3x3o - tecgresa)
Images
Pentisteriruncinated 7-cube Pentisteriruncinated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,3,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bipenticantitruncated 7-cube as t1,2,3,6{4,35} Tericelliprismated hepteract (acronym: tecpasa) (Jonathan Bowers)Klitzing, (x4o3o3x3x3x3o - tecpasa)
Images
Pentisteriruncitruncated 7-cube Pentisteriruncitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,3,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges40320Vertices10080Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Tericelliprismatotruncated hepteract (acronym: tecpetsa) (Jonathan Bowers)Klitzing, (x4x3o3x3x3x3o - tecpetsa)
Images
Pentisteriruncicantellated 7-cube Pentisteriruncicantellated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,2,3,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdges40320Vertices10080Vertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Bipentiruncicantitruncated 7-cube as t1,2,3,4,6{4,35} Tericelliprismatorhombated hepteract (acronym: tocpresa) (Jonathan Bowers)Klitzing, (x4o3x3x3x3x3o - tocpresa)
Images
Pentisteriruncicantitruncated 7-cube Pentisteriruncicantitruncated 7-cubeTypeuniform 7-polytopeSchläfli symbol t0,1,2,3,4,5{4,35}Coxeter-Dynkin diagrams6-faces5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB7, [4,35]Propertiesconvex
Alternate names Great hepteract (acronym: gotesa) (Jonathan Bowers)Klitzing, (x4x3x3x3x3x3o - gotesa)
Images
Related polytopes These polytopes are a part of a set of 127 uniform 7-polytopes with B7 symmetry.
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