Steric 6-cube edit Alternate names edit Runcinated demihexeract/6-demicube Small prismated hemihexeract (Acronym sophax) (Jonathan Bowers)[1] Cartesian coordinates edit The Cartesian coordinates for the 480 vertices of a steric 6-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±1,±1,±3) with an odd number of plus signs.
Images edit Related polytopes edit Dimensional family of steric n-cubes n 5 6 7 8 [1+ ,4,3n-2 ]n-3,1 ] [1+ ,4,33 ]2,1 ] [1+ ,4,34 ]3,1 ] [1+ ,4,35 ]4,1 ] [1+ ,4,36 ]5,1 ] Steric Coxeter Schläfli h4 {4,33 } h4 {4,34 } h4 {4,35 } h4 {4,36 }
Stericantic 6-cube edit Alternate names edit Runcitruncated demihexeract/6-demicube Prismatotruncated hemihexeract (Acronym pithax) (Jonathan Bowers)[2] Cartesian coordinates edit The Cartesian coordinates for the 2880 vertices of a stericantic 6-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±3,±3,±5) with an odd number of plus signs.
Images edit Steriruncic 6-cube edit Alternate names edit Runcicantellated demihexeract/6-demicube Prismatorhombated hemihexeract (Acronym prohax) (Jonathan Bowers)[3] Cartesian coordinates edit The Cartesian coordinates for the 1920 vertices of a steriruncic 6-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±1,±3,±5) with an odd number of plus signs.
Images edit Steriruncicantic 6-cube edit Steriruncicantic 6-cube Type uniform 6-polytope Schläfli symbol t0,1,2,3 {3,32,1 }2,3,4 {4,34 } Coxeter-Dynkin diagram 5-faces 4-faces Cells Faces Edges 17280 Vertices 5760 Vertex figure Coxeter groups D6 , [33,1,1 ] Properties convex
Alternate names edit Runcicantitruncated demihexeract/6-demicube Great prismated hemihexeract (Acronym gophax) (Jonathan Bowers)[4] Cartesian coordinates edit The Cartesian coordinates for the 5760 vertices of a steriruncicantic 6-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±3,±5,±7) with an odd number of plus signs.
Images edit Related polytopes edit There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:
D6 polytopes h{4,34 } h2 {4,34 } h3 {4,34 } h4 {4,34 } h5 {4,34 } h2,3 {4,34 } h2,4 {4,34 } h2,5 {4,34 } h3,4 {4,34 } h3,5 {4,34 } h4,5 {4,34 } h2,3,4 {4,34 } h2,3,5 {4,34 } h2,4,5 {4,34 } h3,4,5 {4,34 } h2,3,4,5 {4,34 }
Notes edit ^ Klitzing, (x3o3o *b3o3x3o - sophax) ^ Klitzing, (x3x3o *b3o3x3o - pithax) ^ Klitzing, (x3o3o *b3x3x3o - prohax) ^ Klitzing, (x3x3o *b3x3x3o - gophax) 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
steric, cubes, demicube, steric, cube, stericantic, cube, steriruncic, cube, stericruncicantic, cube, orthogonal, projections, coxeter, plane, dimensional, geometry, steric, cube, convex, uniform, polytope, there, unique, steric, forms, cube, contents, steric,. 6 demicube Steric 6 cube Stericantic 6 cube Steriruncic 6 cube Stericruncicantic 6 cube Orthogonal projections in D6 Coxeter plane In six dimensional geometry a steric 6 cube is a convex uniform 6 polytope There are unique 4 steric forms of the 6 cube Contents 1 Steric 6 cube 1 1 Alternate names 1 2 Cartesian coordinates 1 3 Images 1 4 Related polytopes 2 Stericantic 6 cube 2 1 Alternate names 2 2 Cartesian coordinates 2 3 Images 3 Steriruncic 6 cube 3 1 Alternate names 3 2 Cartesian coordinates 3 3 Images 4 Steriruncicantic 6 cube 4 1 Alternate names 4 2 Cartesian coordinates 4 3 Images 5 Related polytopes 6 Notes 7 References 8 External linksSteric 6 cube editSteric 6 cube Type uniform 6 polytope Schlafli symbol t0 3 3 33 1 h4 4 34 Coxeter Dynkin diagram nbsp nbsp 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 3360 Vertices 480 Vertex figure Coxeter groups D6 33 1 1 Properties convex Alternate names edit Runcinated demihexeract 6 demicube Small prismated hemihexeract Acronym sophax Jonathan Bowers 1 Cartesian coordinates edit The Cartesian coordinates for the 480 vertices of a steric 6 cube centered at the origin are coordinate permutations 1 1 1 1 1 3 with an odd number of plus signs Images edit orthographic projections Coxeter plane B6 Graph nbsp Dihedral symmetry 12 2 Coxeter plane D6 D5 Graph nbsp nbsp Dihedral symmetry 10 8 Coxeter plane D4 D3 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Related polytopes edit Dimensional family of steric n cubes n 5 6 7 8 1 4 3n 2 3 3n 3 1 1 4 33 3 32 1 1 4 34 3 33 1 1 4 35 3 34 1 1 4 36 3 35 1 Stericfigure nbsp nbsp nbsp nbsp Coxeter nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Schlafli h4 4 33 h4 4 34 h4 4 35 h4 4 36 Stericantic 6 cube editStericantic 6 cube Type uniform 6 polytope Schlafli symbol t0 1 3 3 33 1 h2 4 4 34 Coxeter Dynkin diagram nbsp nbsp 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 12960 Vertices 2880 Vertex figure Coxeter groups D6 33 1 1 Properties convex Alternate names edit Runcitruncated demihexeract 6 demicube Prismatotruncated hemihexeract Acronym pithax Jonathan Bowers 2 Cartesian coordinates edit The Cartesian coordinates for the 2880 vertices of a stericantic 6 cube centered at the origin are coordinate permutations 1 1 1 3 3 5 with an odd number of plus signs Images edit orthographic projections Coxeter plane B6 Graph nbsp Dihedral symmetry 12 2 Coxeter plane D6 D5 Graph nbsp nbsp Dihedral symmetry 10 8 Coxeter plane D4 D3 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncic 6 cube editSteriruncic 6 cube Type uniform 6 polytope Schlafli symbol t0 2 3 3 33 1 h3 4 4 34 Coxeter Dynkin diagram nbsp nbsp 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 7680 Vertices 1920 Vertex figure Coxeter groups D6 33 1 1 Properties convex Alternate names edit Runcicantellated demihexeract 6 demicube Prismatorhombated hemihexeract Acronym prohax Jonathan Bowers 3 Cartesian coordinates edit The Cartesian coordinates for the 1920 vertices of a steriruncic 6 cube centered at the origin are coordinate permutations 1 1 1 1 3 5 with an odd number of plus signs Images edit orthographic projections Coxeter plane B6 Graph nbsp Dihedral symmetry 12 2 Coxeter plane D6 D5 Graph nbsp nbsp Dihedral symmetry 10 8 Coxeter plane D4 D3 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Steriruncicantic 6 cube editSteriruncicantic 6 cube Type uniform 6 polytope Schlafli symbol t0 1 2 3 3 32 1 h2 3 4 4 34 Coxeter Dynkin diagram nbsp nbsp 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 17280 Vertices 5760 Vertex figure Coxeter groups D6 33 1 1 Properties convex Alternate names edit Runcicantitruncated demihexeract 6 demicube Great prismated hemihexeract Acronym gophax Jonathan Bowers 4 Cartesian coordinates edit The Cartesian coordinates for the 5760 vertices of a steriruncicantic 6 cube centered at the origin are coordinate permutations 1 1 1 3 5 7 with an odd number of plus signs Images edit orthographic projections Coxeter plane B6 Graph nbsp Dihedral symmetry 12 2 Coxeter plane D6 D5 Graph nbsp nbsp Dihedral symmetry 10 8 Coxeter plane D4 D3 Graph nbsp nbsp Dihedral symmetry 6 4 Coxeter plane A5 A3 Graph nbsp nbsp Dihedral symmetry 6 4 Related polytopes editThere are 47 uniform polytopes with D6 symmetry 31 are shared by the B6 symmetry and 16 are unique D6 polytopes nbsp h 4 34 nbsp h2 4 34 nbsp h3 4 34 nbsp h4 4 34 nbsp h5 4 34 nbsp h2 3 4 34 nbsp h2 4 4 34 nbsp h2 5 4 34 nbsp h3 4 4 34 nbsp h3 5 4 34 nbsp h4 5 4 34 nbsp h2 3 4 4 34 nbsp h2 3 5 4 34 nbsp h2 4 5 4 34 nbsp h3 4 5 4 34 nbsp h2 3 4 5 4 34 Notes edit Klitzing x3o3o b3o3x3o sophax Klitzing x3x3o b3o3x3o pithax Klitzing x3o3o b3x3x3o prohax Klitzing x3x3o b3x3x3o gophax 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 x3o3o b3o3x3o sophax x3x3o b3o3x3o pithax x3o3o b3x3x3o prohax x3x3o b3x3x3o gophaxExternal links editWeisstein Eric W Hypercube MathWorld Polytopes 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 Steric 6 cubes amp oldid 1148116639 Steriruncic 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.