Cantellated 5-cube edit Cantellated 5-cube Type Uniform 5-polytope Schläfli symbol rr{4,3,3,3} = r { 4 3 , 3 , 3 } {\displaystyle r\left\{{\begin{array}{l}4\\3,3,3\end{array}}\right\}} Coxeter-Dynkin diagram 4-faces 122 10 Cells 680 40 Faces 1520 80 Edges 1280 320+960 Vertices 320 Vertex figure Coxeter group B5 [4,3,3,3] Properties convex , uniform
Alternate names edit Small rhombated penteract (Acronym: sirn) (Jonathan Bowers) Coordinates edit The Cartesian coordinates of the vertices of a cantellated 5-cube having edge length 2 are all permutations of:
( ± 1 , ± 1 , ± ( 1 + 2 ) , ± ( 1 + 2 ) , ± ( 1 + 2 ) ) {\displaystyle \left(\pm 1,\ \pm 1,\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}})\right)} Images edit Bicantellated 5-cube edit Bicantellated 5-cube Type Uniform 5-polytope Schläfli symbols 2rr{4,3,3,3} = r { 3 , 4 3 , 3 } {\displaystyle r\left\{{\begin{array}{l}3,4\\3,3\end{array}}\right\}} 2,1,1 } = r { 3 , 3 3 3 } {\displaystyle r\left\{{\begin{array}{l}3,3\\3\\3\end{array}}\right\}} Coxeter-Dynkin diagrams 4-faces 122 10 Cells 840 40 Faces 2160 240 Edges 1920 960+960 Vertices 480 Vertex figure Coxeter groups B5 , [3,3,3,4]5 , [32,1,1 ] Properties convex , uniform
In five-dimensional geometry , a bicantellated 5-cube is a uniform 5-polytope .
Alternate names edit Bicantellated penteract, bicantellated 5-orthoplex, or bicantellated pentacross Small birhombated penteractitriacontiditeron (Acronym: sibrant) (Jonathan Bowers) Coordinates edit The Cartesian coordinates of the vertices of a bicantellated 5-cube having edge length 2 are all permutations of:
(0,1,1,2,2) Images edit
Cantitruncated 5-cube edit Cantitruncated 5-cube Type Uniform 5-polytope Schläfli symbol tr{4,3,3,3} = t { 4 3 , 3 , 3 } {\displaystyle t\left\{{\begin{array}{l}4\\3,3,3\end{array}}\right\}} Coxeter-Dynkin 4-faces 122 10 Cells 680 40 Faces 1520 80 Edges 1600 320+320+960 Vertices 640 Vertex figure Coxeter group B5 [4,3,3,3] Properties convex , uniform
Alternate names edit Tricantitruncated 5-orthoplex / tricantitruncated pentacross Great rhombated penteract (girn) (Jonathan Bowers) Coordinates edit The Cartesian coordinates of the vertices of a cantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:
( 1 , 1 + 2 , 1 + 2 2 , 1 + 2 2 , 1 + 2 2 ) {\displaystyle \left(1,\ 1+{\sqrt {2}},\ 1+2{\sqrt {2}},\ 1+2{\sqrt {2}},\ 1+2{\sqrt {2}}\right)} Images edit Related polytopes edit It is third in a series of cantitruncated hypercubes:
Bicantitruncated 5-cube edit Bicantitruncated 5-cube Type uniform 5-polytope Schläfli symbol 2tr{3,3,3,4} = t { 3 , 4 3 , 3 } {\displaystyle t\left\{{\begin{array}{l}3,4\\3,3\end{array}}\right\}} 2,1,1 } = t { 3 , 3 3 3 } {\displaystyle t\left\{{\begin{array}{l}3,3\\3\\3\end{array}}\right\}} Coxeter-Dynkin diagrams 4-faces 122 10 Cells 840 40 Faces 2160 240 Edges 2400 960+480+960 Vertices 960 Vertex figure Coxeter groups B5 , [3,3,3,4]5 , [32,1,1 ] Properties convex , uniform
Alternate names edit Bicantitruncated penteract Bicantitruncated pentacross Great birhombated penteractitriacontiditeron (Acronym: gibrant) (Jonathan Bowers) Coordinates edit Cartesian coordinates for the vertices of a bicantitruncated 5-cube, centered at the origin, are all sign and coordinate permutations of
(±3,±3,±2,±1,0) Images edit Related polytopes edit These polytopes are from a set of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex .
B5 polytopes β5 t1 β5 t2 γ5 t1 γ5 γ5 t0,1 β5 t0,2 β5 t1,2 β5 t0,3 β5 t1,3 γ5 t1,2 γ5 t0,4 γ5 t0,3 γ5 t0,2 γ5 t0,1 γ5 t0,1,2 β5 t0,1,3 β5 t0,2,3 β5 t1,2,3 γ5 t0,1,4 β5 t0,2,4 γ5 t0,2,3 γ5 t0,1,4 γ5 t0,1,3 γ5 t0,1,2 γ5 t0,1,2,3 β5 t0,1,2,4 β5 t0,1,3,4 γ5 t0,1,2,4 γ5 t0,1,2,3 γ5 t0,1,2,3,4 γ5
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 , editied 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. "5D uniform polytopes (polytera)". External links edit , George Olshevsky. Polytopes of Various Dimensions, Jonathan Bowers Runcinated uniform polytera (spid), Jonathan Bowers Multi-dimensional Glossary
cantellated, cubes, cube, cantellated, cube, bicantellated, cube, cantellated, orthoplex5, orthoplex, cantitruncated, cube, bicantitruncated, cube, cantitruncated, orthoplexorthogonal, projections, coxeter, planein, dimensional, geometry, cantellated, cube, co. 5 cube Cantellated 5 cube Bicantellated 5 cube Cantellated 5 orthoplex5 orthoplex Cantitruncated 5 cube Bicantitruncated 5 cube Cantitruncated 5 orthoplexOrthogonal projections in B5 Coxeter planeIn six dimensional geometry a cantellated 5 cube is a convex uniform 5 polytope being a cantellation of the regular 5 cube There are 6 unique cantellation for the 5 cube including truncations Half of them are more easily constructed from the dual 5 orthoplex Contents 1 Cantellated 5 cube 1 1 Alternate names 1 2 Coordinates 1 3 Images 2 Bicantellated 5 cube 2 1 Alternate names 2 2 Coordinates 2 3 Images 3 Cantitruncated 5 cube 3 1 Alternate names 3 2 Coordinates 3 3 Images 3 4 Related polytopes 4 Bicantitruncated 5 cube 4 1 Alternate names 4 2 Coordinates 4 3 Images 5 Related polytopes 6 References 7 External linksCantellated 5 cube editCantellated 5 cubeType Uniform 5 polytopeSchlafli symbol rr 4 3 3 3 r 43 3 3 displaystyle r left begin array l 4 3 3 3 end array right nbsp Coxeter Dynkin diagram nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 faces 122 10 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 80 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 32 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Cells 680 40 nbsp nbsp nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp nbsp nbsp 160 nbsp nbsp nbsp nbsp nbsp nbsp 160 nbsp nbsp nbsp nbsp nbsp nbsp Faces 1520 80 nbsp nbsp nbsp nbsp 480 nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp 640 nbsp nbsp nbsp nbsp Edges 1280 320 960Vertices 320Vertex figure nbsp Coxeter group B5 4 3 3 3 Properties convex uniformAlternate names edit Small rhombated penteract Acronym sirn Jonathan Bowers Coordinates edit The Cartesian coordinates of the vertices of a cantellated 5 cube having edge length 2 are all permutations of 1 1 1 2 1 2 1 2 displaystyle left pm 1 pm 1 pm 1 sqrt 2 pm 1 sqrt 2 pm 1 sqrt 2 right nbsp Images edit orthographic projections Coxeter plane B5 B4 D5 B3 D4 A2Graph nbsp nbsp nbsp Dihedral symmetry 10 8 6 Coxeter plane B2 A3Graph nbsp nbsp Dihedral symmetry 4 4 Bicantellated 5 cube editBicantellated 5 cubeType Uniform 5 polytopeSchlafli symbols 2rr 4 3 3 3 r 3 43 3 displaystyle r left begin array l 3 4 3 3 end array right nbsp r 32 1 1 r 3 333 displaystyle r left begin array l 3 3 3 3 end array right nbsp Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 faces 122 10 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 80 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 32 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Cells 840 40 nbsp nbsp nbsp nbsp nbsp nbsp 240 nbsp nbsp nbsp nbsp nbsp nbsp 160 nbsp nbsp nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp nbsp nbsp 80 nbsp nbsp nbsp nbsp nbsp nbsp Faces 2160 240 nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp 960 nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp Edges 1920 960 960Vertices 480Vertex figure nbsp Coxeter groups B5 3 3 3 4 D5 32 1 1 Properties convex uniformIn five dimensional geometry a bicantellated 5 cube is a uniform 5 polytope Alternate names edit Bicantellated penteract bicantellated 5 orthoplex or bicantellated pentacross Small birhombated penteractitriacontiditeron Acronym sibrant Jonathan Bowers Coordinates edit The Cartesian coordinates of the vertices of a bicantellated 5 cube having edge length 2 are all permutations of 0 1 1 2 2 Images edit orthographic projections Coxeter plane B5 B4 D5 B3 D4 A2Graph nbsp nbsp nbsp Dihedral symmetry 10 8 6 Coxeter plane B2 A3Graph nbsp nbsp Dihedral symmetry 4 4 Cantitruncated 5 cube editCantitruncated 5 cubeType Uniform 5 polytopeSchlafli symbol tr 4 3 3 3 t 43 3 3 displaystyle t left begin array l 4 3 3 3 end array right nbsp Coxeter Dynkindiagram nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 faces 122 10 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 80 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 32 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Cells 680 40 nbsp nbsp nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp nbsp nbsp 160 nbsp nbsp nbsp nbsp nbsp nbsp 160 nbsp nbsp nbsp nbsp nbsp nbsp Faces 1520 80 nbsp nbsp nbsp nbsp 480 nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp 640 nbsp nbsp nbsp nbsp Edges 1600 320 320 960Vertices 640Vertex figure nbsp Coxeter group B5 4 3 3 3 Properties convex uniformAlternate names edit Tricantitruncated 5 orthoplex tricantitruncated pentacross Great rhombated penteract girn Jonathan Bowers Coordinates edit The Cartesian coordinates of the vertices of a cantitruncated 5 cube having an edge length of 2 are given by all permutations of coordinates and sign of 1 1 2 1 22 1 22 1 22 displaystyle left 1 1 sqrt 2 1 2 sqrt 2 1 2 sqrt 2 1 2 sqrt 2 right nbsp Images edit orthographic projections Coxeter plane B5 B4 D5 B3 D4 A2Graph nbsp nbsp nbsp Dihedral symmetry 10 8 6 Coxeter plane B2 A3Graph nbsp nbsp Dihedral symmetry 4 4 Related polytopes edit It is third in a series of cantitruncated hypercubes Petrie polygon projections nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Truncated cuboctahedron Cantitruncated tesseract Cantitruncated 5 cube Cantitruncated 6 cube Cantitruncated 7 cube Cantitruncated 8 cube 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 Bicantitruncated 5 cube editBicantitruncated 5 cubeType uniform 5 polytopeSchlafli symbol 2tr 3 3 3 4 t 3 43 3 displaystyle t left begin array l 3 4 3 3 end array right nbsp t 32 1 1 t 3 333 displaystyle t left begin array l 3 3 3 3 end array right nbsp Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 faces 122 10 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 80 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 32 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Cells 840 40 nbsp nbsp nbsp nbsp nbsp nbsp 240 nbsp nbsp nbsp nbsp nbsp nbsp 160 nbsp nbsp nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp nbsp nbsp 80 nbsp nbsp nbsp nbsp nbsp nbsp Faces 2160 240 nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp 960 nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp 320 nbsp nbsp nbsp nbsp Edges 2400 960 480 960Vertices 960Vertex figure nbsp Coxeter groups B5 3 3 3 4 D5 32 1 1 Properties convex uniformAlternate names edit Bicantitruncated penteract Bicantitruncated pentacross Great birhombated penteractitriacontiditeron Acronym gibrant Jonathan Bowers Coordinates edit Cartesian coordinates for the vertices of a bicantitruncated 5 cube centered at the origin are all sign and coordinate permutations of 3 3 2 1 0 Images edit orthographic projections Coxeter plane B5 B4 D5 B3 D4 A2Graph nbsp nbsp nbsp Dihedral symmetry 10 8 6 Coxeter plane B2 A3Graph nbsp nbsp Dihedral symmetry 4 4 Related polytopes editThese polytopes are from a set of 31 uniform 5 polytopes generated from the regular 5 cube or 5 orthoplex B5 polytopes nbsp b5 nbsp t1b5 nbsp t2g5 nbsp t1g5 nbsp g5 nbsp t0 1b5 nbsp t0 2b5 nbsp t1 2b5 nbsp t0 3b5 nbsp t1 3g5 nbsp t1 2g5 nbsp t0 4g5 nbsp t0 3g5 nbsp t0 2g5 nbsp t0 1g5 nbsp t0 1 2b5 nbsp t0 1 3b5 nbsp t0 2 3b5 nbsp t1 2 3g5 nbsp t0 1 4b5 nbsp t0 2 4g5 nbsp t0 2 3g5 nbsp t0 1 4g5 nbsp t0 1 3g5 nbsp t0 1 2g5 nbsp t0 1 2 3b5 nbsp t0 1 2 4b5 nbsp t0 1 3 4g5 nbsp t0 1 2 4g5 nbsp t0 1 2 3g5 nbsp t0 1 2 3 4g5References editH S M Coxeter H S M Coxeter Regular Polytopes 3rd Edition Dover New York 1973 Kaleidoscopes Selected Writings of H S M Coxeter editied 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 5D uniform polytopes polytera o3o3x3o4x sirn o3x3o3x4o sibrant o3o3x3x4x girn o3x3x3x4o gibrantExternal links editGlossary for hyperspace George Olshevsky Polytopes of Various Dimensions Jonathan Bowers Runcinated uniform polytera spid Jonathan Bowers Multi dimensional GlossaryvteFundamental convex regular and uniform polytopes in dimensions 2 10Family An Bn I2 p Dn E6 E7 E8 F4 G2 HnRegular polygon Triangle Square p gon Hexagon PentagonUniform polyhedron Tetrahedron Octahedron Cube Demicube Dodecahedron IcosahedronUniform polychoron Pentachoron 16 cell Tesseract Demitesseract 24 cell 120 cell 600 cellUniform 5 polytope 5 simplex 5 orthoplex 5 cube 5 demicubeUniform 6 polytope 6 simplex 6 orthoplex 6 cube 6 demicube 122 221Uniform 7 polytope 7 simplex 7 orthoplex 7 cube 7 demicube 132 231 321Uniform 8 polytope 8 simplex 8 orthoplex 8 cube 8 demicube 142 241 421Uniform 9 polytope 9 simplex 9 orthoplex 9 cube 9 demicubeUniform 10 polytope 10 simplex 10 orthoplex 10 cube 10 demicubeUniform n polytope n simplex n orthoplex n cube n demicube 1k2 2k1 k21 n pentagonal polytopeTopics Polytope families Regular polytope List of regular polytopes and compounds Retrieved from https en wikipedia org w index php title Cantellated 5 cubes amp oldid 1192102435 Cantitruncated 5 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.