Orthogonal projections in B6 Coxeter plane 7-cube Stericated 7-cube Bistericated 7-cube Steritruncated 7-cube Bisteritruncated 7-cube Stericantellated 7-cube Bistericantellated 7-cube Stericantitruncated 7-cube Bistericantitruncated 7-cube Steriruncinated 7-cube Steriruncitruncated 7-cube Steriruncicantellated 7-cube Bisteriruncitruncated 7-cube Steriruncicantitruncated 7-cube Bisteriruncicantitruncated 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 edit Alternate names edit Small cellated hepteract (acronym: ) (Jonathan Bowers)[1] Images edit Bistericated 7-cube edit Alternate names edit Small bicellated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)[2] Images edit Steritruncated 7-cube edit Alternate names edit Cellitruncated hepteract (acronym: ) (Jonathan Bowers)[3] Images edit Bisteritruncated 7-cube edit Alternate names edit Bicellitruncated hepteract (acronym: ) (Jonathan Bowers)[4] Images edit Stericantellated 7-cube edit Alternate names edit Cellirhombated hepteract (acronym: ) (Jonathan Bowers)[5] Images edit Bistericantellated 7-cube edit Alternate names edit Bicellirhombihepteract (acronym: ) (Jonathan Bowers)[6] Images edit Stericantitruncated 7-cube edit Alternate names edit Celligreatorhombated hepteract (acronym: ) (Jonathan Bowers)[7] Images edit Bistericantitruncated 7-cube edit Alternate names edit Bicelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)[8] Images edit Steriruncinated 7-cube edit Alternate names edit Celliprismated hepteract (acronym: ) (Jonathan Bowers)[9] Images edit Steriruncitruncated 7-cube edit Alternate names edit Celliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)[10] Images edit Steriruncicantellated 7-cube edit Alternate names edit Celliprismatorhombated hepteract (acronym: ) (Jonathan Bowers)[11] Images edit Bisteriruncitruncated 7-cube edit Alternate names edit Bicelliprismatotruncated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)[12] Images edit Steriruncicantitruncated 7-cube edit Alternate names edit Great cellated hepteract (acronym: ) (Jonathan Bowers)[13] Images edit Bisteriruncicantitruncated 7-cube edit Alternate names edit Great bicellated hepteractihecatonicosoctaexon (Acronym ) (Jonathan Bowers) [14] Images edit Notes edit ^ Klitizing, (x3o3o3o3x3o4o - ) ^ Klitizing, (x3o3x3o3x3o4o - ) ^ Klitizing, (x3x3o3o3x3o4o - ) ^ Klitizing, (o3x3x3o3o3x4o - ) ^ Klitizing, (x3o3x3o3x3o4o - ) ^ Klitizing, (o3x3o3x3o3x4o - ) ^ Klitizing, (x3x3x3o3x3o4o - ) ^ Klitizing, (o3x3x3x3o3x4o - ) ^ Klitizing, (x3o3o3x3x3o4o - ) ^ Klitizing, (x3x3x3o3x3o4o - ) ^ Klitizing, (x3o3x3x3x3o4o - ) ^ Klitizing, (o3x3x3o3x3x4o - ) ^ Klitizing, (x3x3x3x3x3o4o - ) ^ Klitizing, (o3x3x3x3x3x4o - ) References edit 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 Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1] (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. Klitzing, Richard. "7D uniform polytopes (polyexa)". External links edit Polytopes of Various Dimensions Multi-dimensional Glossary
stericated, cubes, orthogonal, projections, coxeter, plane, cube, stericated, cube, bistericated, cube, steritruncated, cube, bisteritruncated, cube, stericantellated, cube, bistericantellated, cube, stericantitruncated, cube, bistericantitruncated, cube, ster. Orthogonal projections in B6 Coxeter plane 7 cube Stericated 7 cube Bistericated 7 cube Steritruncated 7 cube Bisteritruncated 7 cube Stericantellated 7 cube Bistericantellated 7 cube Stericantitruncated 7 cube Bistericantitruncated 7 cube Steriruncinated 7 cube Steriruncitruncated 7 cube Steriruncicantellated 7 cube Bisteriruncitruncated 7 cube Steriruncicantitruncated 7 cube Bisteriruncicantitruncated 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 Contents 1 Stericated 7 cube 1 1 Alternate names 1 2 Images 2 Bistericated 7 cube 2 1 Alternate names 2 2 Images 3 Steritruncated 7 cube 3 1 Alternate names 3 2 Images 4 Bisteritruncated 7 cube 4 1 Alternate names 4 2 Images 5 Stericantellated 7 cube 5 1 Alternate names 5 2 Images 6 Bistericantellated 7 cube 6 1 Alternate names 6 2 Images 7 Stericantitruncated 7 cube 7 1 Alternate names 7 2 Images 8 Bistericantitruncated 7 cube 8 1 Alternate names 8 2 Images 9 Steriruncinated 7 cube 9 1 Alternate names 9 2 Images 10 Steriruncitruncated 7 cube 10 1 Alternate names 10 2 Images 11 Steriruncicantellated 7 cube 11 1 Alternate names 11 2 Images 12 Bisteriruncitruncated 7 cube 12 1 Alternate names 12 2 Images 13 Steriruncicantitruncated 7 cube 13 1 Alternate names 13 2 Images 14 Bisteriruncicantitruncated 7 cube 14 1 Alternate names 14 2 Images 15 Notes 16 References 17 External linksStericated 7 cube editStericated 7 cube Type uniform 7 polytope Schlafli symbol t0 4 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Small cellated hepteract acronym Jonathan Bowers 1 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Bistericated 7 cube editbistericated 7 cube Type uniform 7 polytope Schlafli symbol t1 5 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Small bicellated hepteractihecatonicosoctaexon acronym Jonathan Bowers 2 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steritruncated 7 cube editsteritruncated 7 cube Type uniform 7 polytope Schlafli symbol t0 1 4 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Cellitruncated hepteract acronym Jonathan Bowers 3 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Bisteritruncated 7 cube editbisteritruncated 7 cube Type uniform 7 polytope Schlafli symbol t1 2 5 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Bicellitruncated hepteract acronym Jonathan Bowers 4 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Stericantellated 7 cube editStericantellated 7 cube Type uniform 7 polytope Schlafli symbol t0 2 4 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Cellirhombated hepteract acronym Jonathan Bowers 5 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Bistericantellated 7 cube editBistericantellated 7 cube Type uniform 7 polytope Schlafli symbol t1 3 5 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Bicellirhombihepteract acronym Jonathan Bowers 6 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Stericantitruncated 7 cube editstericantitruncated 7 cube Type uniform 7 polytope Schlafli symbol t0 1 2 4 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Celligreatorhombated hepteract acronym Jonathan Bowers 7 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Bistericantitruncated 7 cube editbistericantitruncated 7 cube Type uniform 7 polytope Schlafli symbol t1 2 3 5 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Bicelligreatorhombated hepteract acronym Jonathan Bowers 8 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncinated 7 cube editSteriruncinated 7 cube Type uniform 7 polytope Schlafli symbol t0 3 4 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Celliprismated hepteract acronym Jonathan Bowers 9 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncitruncated 7 cube editsteriruncitruncated 7 cube Type uniform 7 polytope Schlafli symbol t0 1 3 4 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Celliprismatotruncated hepteract acronym Jonathan Bowers 10 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncicantellated 7 cube editsteriruncicantellated 7 cube Type uniform 7 polytope Schlafli symbol t0 2 3 4 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Celliprismatorhombated hepteract acronym Jonathan Bowers 11 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Bisteriruncitruncated 7 cube editbisteriruncitruncated 7 cube Type uniform 7 polytope Schlafli symbol t1 2 4 5 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Bicelliprismatotruncated hepteractihecatonicosoctaexon acronym Jonathan Bowers 12 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncicantitruncated 7 cube editsteriruncicantitruncated 7 cube Type uniform 7 polytope Schlafli symbol t0 1 2 3 4 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Great cellated hepteract acronym Jonathan Bowers 13 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph too complex too complex Dihedral symmetry 6 4 Bisteriruncicantitruncated 7 cube editbisteriruncicantitruncated 7 cube Type uniform 7 polytope Schlafli symbol t1 2 3 4 5 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces 5 faces 4 faces Cells Faces Edges Vertices Vertex figure Coxeter groups B7 4 35 Properties convex Alternate names edit Great bicellated hepteractihecatonicosoctaexon Acronym Jonathan Bowers 14 Images edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4 Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3 Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Notes edit Klitizing x3o3o3o3x3o4o Klitizing x3o3x3o3x3o4o Klitizing x3x3o3o3x3o4o Klitizing o3x3x3o3o3x4o Klitizing x3o3x3o3x3o4o Klitizing o3x3o3x3o3x4o Klitizing x3x3x3o3x3o4o Klitizing o3x3x3x3o3x4o Klitizing x3o3o3x3x3o4o Klitizing x3x3x3o3x3o4o Klitizing x3o3x3x3x3o4o Klitizing o3x3x3o3x3x4o Klitizing x3x3x3x3x3o4o Klitizing o3x3x3x3x3x4o References editH 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 Ivic Weiss Wiley Interscience Publication 1995 ISBN 978 0 471 01003 6 1 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 Klitzing Richard 7D uniform polytopes polyexa x3o3o3o3x3o4o x3o3x3o3x3o4o x3x3o3o3x3o4o o3x3x3o3o3x4o x3o3x3o3x3o4o o3x3o3x3o3x4o x3x3x3o3x3o4o o3x3x3x3o3x4o x3o3o3x3x3o4o x3x3x3o3x3o4o x3o3x3x3x3o4o o3x3x3o3x3x4o x3x3x3x3x3o4o o3x3x3x3x3x4o External links editPolytopes of Various Dimensions Multi dimensional Glossary vteFundamental convex regular and uniform polytopes in dimensions 2 10 Family An Bn I2 p Dn E6 E7 E8 F4 G2 Hn Regular polygon Triangle Square p gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron Cube Demicube Dodecahedron Icosahedron Uniform polychoron Pentachoron 16 cell Tesseract Demitesseract 24 cell 120 cell 600 cell Uniform 5 polytope 5 simplex 5 orthoplex 5 cube 5 demicube Uniform 6 polytope 6 simplex 6 orthoplex 6 cube 6 demicube 122 221 Uniform 7 polytope 7 simplex 7 orthoplex 7 cube 7 demicube 132 231 321 Uniform 8 polytope 8 simplex 8 orthoplex 8 cube 8 demicube 142 241 421 Uniform 9 polytope 9 simplex 9 orthoplex 9 cube 9 demicube Uniform 10 polytope 10 simplex 10 orthoplex 10 cube 10 demicube Uniform n polytope n simplex n orthoplex n cube n demicube 1k2 2k1 k21 n pentagonal polytope Topics Polytope families Regular polytope List of regular polytopes and compounds Retrieved from https en wikipedia org w index php title Stericated 7 cubes amp oldid 1214136209 Stericated 7 cube, wikipedia, wiki , book, books, library,
article , read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.