6-cube Stericated 6-cube Steritruncated 6-cube Stericantellated 6-cube Stericantitruncated 6-cube Steriruncinated 6-cube Steriruncitruncated 6-cube Steriruncicantellated 6-cube Steriruncicantitruncated 6-cube Orthogonal projections in B6 Coxeter plane
In six-dimensional geometry , a stericated 6-cube is a convex uniform 6-polytope , constructed as a sterication (4th order truncation) of the regular 6-cube .
There are 8 unique sterications for the 6-cube with permutations of truncations, cantellations, and runcinations.
Stericated 6-cube edit Alternate names edit Small cellated hexeract (Acronym: scox) (Jonathan Bowers)[1] Images edit Steritruncated 6-cube edit Steritruncated 6-cube Type uniform 6-polytope Schläfli symbol t0,1,4 {4,3,3,3,3} Coxeter-Dynkin diagrams 5-faces 4-faces Cells Faces Edges 19200 Vertices 3840 Vertex figure Coxeter groups B6 , [4,3,3,3,3] Properties convex
Alternate names edit Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)[2] Images edit Stericantellated 6-cube edit Alternate names edit Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)[3] Images edit Stericantitruncated 6-cube edit stericantitruncated 6-cube Type uniform 6-polytope Schläfli symbol t0,1,2,4 {4,3,3,3,3} Coxeter-Dynkin diagrams 5-faces 4-faces Cells Faces Edges 46080 Vertices 11520 Vertex figure Coxeter groups B6 , [4,3,3,3,3] Properties convex
Alternate names edit Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)[4] Images edit Steriruncinated 6-cube edit steriruncinated 6-cube Type uniform 6-polytope Schläfli symbol t0,3,4 {4,3,3,3,3} Coxeter-Dynkin diagrams 5-faces 4-faces Cells Faces Edges 15360 Vertices 3840 Vertex figure Coxeter groups B6 , [4,3,3,3,3] Properties convex
Alternate names edit Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)[5] Images edit Steriruncitruncated 6-cube edit Alternate names edit Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)[6] Images edit Steriruncicantellated 6-cube edit steriruncicantellated 6-cube Type uniform 6-polytope Schläfli symbol t0,2,3,4 {4,3,3,3,3} Coxeter-Dynkin diagrams 5-faces 4-faces Cells Faces Edges 40320 Vertices 11520 Vertex figure Coxeter groups B6 , [4,3,3,3,3] Properties convex
Alternate names edit Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)[7] Images edit Steriruncicantitruncated 6-cube edit Alternate names edit Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)[8] Images edit Related polytopes edit These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane , including the regular 6-cube or 6-orthoplex .
B6 polytopes β6 t1 β6 t2 β6 t2 γ6 t1 γ6 γ6 t0,1 β6 t0,2 β6 t1,2 β6 t0,3 β6 t1,3 β6 t2,3 γ6 t0,4 β6 t1,4 γ6 t1,3 γ6 t1,2 γ6 t0,5 γ6 t0,4 γ6 t0,3 γ6 t0,2 γ6 t0,1 γ6 t0,1,2 β6 t0,1,3 β6 t0,2,3 β6 t1,2,3 β6 t0,1,4 β6 t0,2,4 β6 t1,2,4 β6 t0,3,4 β6 t1,2,4 γ6 t1,2,3 γ6 t0,1,5 β6 t0,2,5 β6 t0,3,4 γ6 t0,2,5 γ6 t0,2,4 γ6 t0,2,3 γ6 t0,1,5 γ6 t0,1,4 γ6 t0,1,3 γ6 t0,1,2 γ6 t0,1,2,3 β6 t0,1,2,4 β6 t0,1,3,4 β6 t0,2,3,4 β6 t1,2,3,4 γ6 t0,1,2,5 β6 t0,1,3,5 β6 t0,2,3,5 γ6 t0,2,3,4 γ6 t0,1,4,5 γ6 t0,1,3,5 γ6 t0,1,3,4 γ6 t0,1,2,5 γ6 t0,1,2,4 γ6 t0,1,2,3 γ6 t0,1,2,3,4 β6 t0,1,2,3,5 β6 t0,1,2,4,5 β6 t0,1,2,4,5 γ6 t0,1,2,3,5 γ6 t0,1,2,3,4 γ6 t0,1,2,3,4,5 γ6
Notes edit ^ Klitzing, (x4o3o3o3x3o - scox) ^ Klitzing, (x4x3o3o3x3o - catax) ^ Klitzing, (x4o3x3o3x3o - crax) ^ Klitzing, (x4x3x3o3x3o - cagorx) ^ Klitzing, (x4o3o3x3x3o - copox)) ^ Klitzing, (x4x3o3x3x3o - captix) ^ Klitzing, (x4o3x3x3x3o - coprix) ^ Klitzing, (x4x3x3x3x3o - gocax) 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. "6D uniform polytopes (polypeta)". External links edit Multi-dimensional Glossary
stericated, cubes, cube, stericated, cube, steritruncated, cube, stericantellated, cube, stericantitruncated, cube, steriruncinated, cube, steriruncitruncated, cube, steriruncicantellated, cube, steriruncicantitruncated, cube, orthogonal, projections, coxeter,. 6 cube Stericated 6 cube Steritruncated 6 cube Stericantellated 6 cube Stericantitruncated 6 cube Steriruncinated 6 cube Steriruncitruncated 6 cube Steriruncicantellated 6 cube Steriruncicantitruncated 6 cube Orthogonal projections in B6 Coxeter plane In six dimensional geometry a stericated 6 cube is a convex uniform 6 polytope constructed as a sterication 4th order truncation of the regular 6 cube There are 8 unique sterications for the 6 cube with permutations of truncations cantellations and runcinations Contents 1 Stericated 6 cube 1 1 Alternate names 1 2 Images 2 Steritruncated 6 cube 2 1 Alternate names 2 2 Images 3 Stericantellated 6 cube 3 1 Alternate names 3 2 Images 4 Stericantitruncated 6 cube 4 1 Alternate names 4 2 Images 5 Steriruncinated 6 cube 5 1 Alternate names 5 2 Images 6 Steriruncitruncated 6 cube 6 1 Alternate names 6 2 Images 7 Steriruncicantellated 6 cube 7 1 Alternate names 7 2 Images 8 Steriruncicantitruncated 6 cube 8 1 Alternate names 8 2 Images 9 Related polytopes 10 Notes 11 References 12 External linksStericated 6 cube editStericated 6 cube Type uniform 6 polytope Schlafli symbol 2r2r 4 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 4 faces Cells Faces Edges 5760 Vertices 960 Vertex figure Coxeter groups B6 4 3 3 3 3 Properties convex Alternate names edit Small cellated hexeract Acronym scox Jonathan Bowers 1 Images edit orthographic projections Coxeter plane B6 B5 B4 Graph nbsp nbsp nbsp Dihedral symmetry 12 10 8 Coxeter plane B3 B2 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steritruncated 6 cube editSteritruncated 6 cube Type uniform 6 polytope Schlafli symbol t0 1 4 4 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 4 faces Cells Faces Edges 19200 Vertices 3840 Vertex figure Coxeter groups B6 4 3 3 3 3 Properties convex Alternate names edit Cellirhombated hexeract Acronym catax Jonathan Bowers 2 Images edit orthographic projections Coxeter plane B6 B5 B4 Graph nbsp nbsp nbsp Dihedral symmetry 12 10 8 Coxeter plane B3 B2 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Stericantellated 6 cube editStericantellated 6 cube Type uniform 6 polytope Schlafli symbol 2r2r 4 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 4 faces Cells Faces Edges 28800 Vertices 5760 Vertex figure Coxeter groups B6 4 3 3 3 3 Properties convex Alternate names edit Cellirhombated hexeract Acronym crax Jonathan Bowers 3 Images edit orthographic projections Coxeter plane B6 B5 B4 Graph nbsp nbsp nbsp Dihedral symmetry 12 10 8 Coxeter plane B3 B2 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Stericantitruncated 6 cube editstericantitruncated 6 cube Type uniform 6 polytope Schlafli symbol t0 1 2 4 4 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 4 faces Cells Faces Edges 46080 Vertices 11520 Vertex figure Coxeter groups B6 4 3 3 3 3 Properties convex Alternate names edit Celligreatorhombated hexeract Acronym cagorx Jonathan Bowers 4 Images edit orthographic projections Coxeter plane B6 B5 B4 Graph nbsp nbsp nbsp Dihedral symmetry 12 10 8 Coxeter plane B3 B2 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncinated 6 cube editsteriruncinated 6 cube Type uniform 6 polytope Schlafli symbol t0 3 4 4 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 4 faces Cells Faces Edges 15360 Vertices 3840 Vertex figure Coxeter groups B6 4 3 3 3 3 Properties convex Alternate names edit Celliprismated hexeract Acronym copox Jonathan Bowers 5 Images edit orthographic projections Coxeter plane B6 B5 B4 Graph nbsp nbsp nbsp Dihedral symmetry 12 10 8 Coxeter plane B3 B2 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncitruncated 6 cube editsteriruncitruncated 6 cube Type uniform 6 polytope Schlafli symbol 2t2r 4 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 4 faces Cells Faces Edges 40320 Vertices 11520 Vertex figure Coxeter groups B6 4 3 3 3 3 Properties convex Alternate names edit Celliprismatotruncated hexeract Acronym captix Jonathan Bowers 6 Images edit orthographic projections Coxeter plane B6 B5 B4 Graph nbsp nbsp nbsp Dihedral symmetry 12 10 8 Coxeter plane B3 B2 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncicantellated 6 cube editsteriruncicantellated 6 cube Type uniform 6 polytope Schlafli symbol t0 2 3 4 4 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 4 faces Cells Faces Edges 40320 Vertices 11520 Vertex figure Coxeter groups B6 4 3 3 3 3 Properties convex Alternate names edit Celliprismatorhombated hexeract Acronym coprix Jonathan Bowers 7 Images edit orthographic projections Coxeter plane B6 B5 B4 Graph nbsp nbsp nbsp Dihedral symmetry 12 10 8 Coxeter plane B3 B2 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncicantitruncated 6 cube editSteriuncicantitruncated 6 cube Type uniform 6 polytope Schlafli symbol tr2r 4 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 4 faces Cells Faces Edges 69120 Vertices 23040 Vertex figure Coxeter groups B6 4 3 3 3 3 Properties convex Alternate names edit Great cellated hexeract Acronym gocax Jonathan Bowers 8 Images edit orthographic projections Coxeter plane B6 B5 B4 Graph nbsp nbsp nbsp Dihedral symmetry 12 10 8 Coxeter plane B3 B2 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Related polytopes editThese polytopes are from a set of 63 uniform 6 polytopes generated from the B6 Coxeter plane including the regular 6 cube or 6 orthoplex B6 polytopes nbsp b6 nbsp t1b6 nbsp t2b6 nbsp t2g6 nbsp t1g6 nbsp g6 nbsp t0 1b6 nbsp t0 2b6 nbsp t1 2b6 nbsp t0 3b6 nbsp t1 3b6 nbsp t2 3g6 nbsp t0 4b6 nbsp t1 4g6 nbsp t1 3g6 nbsp t1 2g6 nbsp t0 5g6 nbsp t0 4g6 nbsp t0 3g6 nbsp t0 2g6 nbsp t0 1g6 nbsp t0 1 2b6 nbsp t0 1 3b6 nbsp t0 2 3b6 nbsp t1 2 3b6 nbsp t0 1 4b6 nbsp t0 2 4b6 nbsp t1 2 4b6 nbsp t0 3 4b6 nbsp t1 2 4g6 nbsp t1 2 3g6 nbsp t0 1 5b6 nbsp t0 2 5b6 nbsp t0 3 4g6 nbsp t0 2 5g6 nbsp t0 2 4g6 nbsp t0 2 3g6 nbsp t0 1 5g6 nbsp t0 1 4g6 nbsp t0 1 3g6 nbsp t0 1 2g6 nbsp t0 1 2 3b6 nbsp t0 1 2 4b6 nbsp t0 1 3 4b6 nbsp t0 2 3 4b6 nbsp t1 2 3 4g6 nbsp t0 1 2 5b6 nbsp t0 1 3 5b6 nbsp t0 2 3 5g6 nbsp t0 2 3 4g6 nbsp t0 1 4 5g6 nbsp t0 1 3 5g6 nbsp t0 1 3 4g6 nbsp t0 1 2 5g6 nbsp t0 1 2 4g6 nbsp t0 1 2 3g6 nbsp t0 1 2 3 4b6 nbsp t0 1 2 3 5b6 nbsp t0 1 2 4 5b6 nbsp t0 1 2 4 5g6 nbsp t0 1 2 3 5g6 nbsp t0 1 2 3 4g6 nbsp t0 1 2 3 4 5g6Notes edit Klitzing x4o3o3o3x3o scox Klitzing x4x3o3o3x3o catax Klitzing x4o3x3o3x3o crax Klitzing x4x3x3o3x3o cagorx Klitzing x4o3o3x3x3o copox Klitzing x4x3o3x3x3o captix Klitzing x4o3x3x3x3o coprix Klitzing x4x3x3x3x3o gocax 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 6D uniform polytopes polypeta 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 6 cubes amp oldid 1148116013 Stericantitruncated 6 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.