7-simplex Runcinated 7-simplex Biruncinated 7-simplex Runcitruncated 7-simplex Biruncitruncated 7-simplex Runcicantellated 7-simplex Biruncicantellated 7-simplex Runcicantitruncated 7-simplex Biruncicantitruncated 7-simplex Orthogonal projections in A7 Coxeter plane
In seven-dimensional geometry , a runcinated 7-simplex is a convex uniform 7-polytope with 3rd order truncations (runcination ) of the regular 7-simplex .
There are 8 unique runcinations of the 7-simplex with permutations of truncations, and cantellations.
Runcinated 7-simplex Edit Alternate names Edit Small prismated octaexon (acronym: spo) (Jonathan Bowers)[1] Coordinates Edit The vertices of the runcinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,1,1,2). This construction is based on facets of the runcinated 8-orthoplex.
Images Edit Biruncinated 7-simplex Edit Alternate names Edit Small biprismated octaexon (sibpo) (Jonathan Bowers)[2] Coordinates Edit The vertices of the biruncinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,1,2,2). This construction is based on facets of the biruncinated 8-orthoplex.
Images Edit Runcitruncated 7-simplex Edit Alternate names Edit Prismatotruncated octaexon (acronym: patto) (Jonathan Bowers)[3] Coordinates Edit The vertices of the runcitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,1,2,3). This construction is based on facets of the runcitruncated 8-orthoplex.
Images Edit Biruncitruncated 7-simplex Edit Alternate names Edit Biprismatotruncated octaexon (acronym: bipto) (Jonathan Bowers)[4] Coordinates Edit The vertices of the biruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,2,3,3). This construction is based on facets of the biruncitruncated 8-orthoplex.
Images Edit Runcicantellated 7-simplex Edit Alternate names Edit Prismatorhombated octaexon (acronym: paro) (Jonathan Bowers)[5] Coordinates Edit The vertices of the runcicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,2,3). This construction is based on facets of the runcicantellated 8-orthoplex.
Images Edit Biruncicantellated 7-simplex Edit Alternate names Edit Biprismatorhombated octaexon (acronym: bipro) (Jonathan Bowers) Coordinates Edit The vertices of the biruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,2,3,3). This construction is based on facets of the biruncicantellated 8-orthoplex.
Images Edit Runcicantitruncated 7-simplex Edit runcicantitruncated 7-simplex Type uniform 7-polytope Schläfli symbol t0,1,2,3 {3,3,3,3,3,3} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 5880 Vertices 1680 Vertex figure Coxeter group A7 , [36 ], order 40320 Properties convex
Alternate names Edit Great prismated octaexon (acronym: gapo) (Jonathan Bowers)[6] Coordinates Edit The vertices of the runcicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,3,4). This construction is based on facets of the runcicantitruncated 8-orthoplex.
Images Edit Biruncicantitruncated 7-simplex Edit biruncicantitruncated 7-simplex Type uniform 7-polytope Schläfli symbol t1,2,3,4 {3,3,3,3,3,3} Coxeter-Dynkin diagrams 6-faces 5-faces 4-faces Cells Faces Edges 11760 Vertices 3360 Vertex figure Coxeter group A7 , [36 ], order 40320 Properties convex
Alternate names Edit Great biprismated octaexon (acronym: gibpo) (Jonathan Bowers)[7] Coordinates Edit The vertices of the biruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,3,4,4). This construction is based on facets of the biruncicantitruncated 8-orthoplex.
Images Edit Related polytopes Edit These polytopes are among 71 uniform 7-polytopes with A7 symmetry.
A7 polytopes t0 t1 t2 t3 t0,1 t0,2 t1,2 t0,3 t1,3 t2,3 t0,4 t1,4 t2,4 t0,5 t1,5 t0,6 t0,1,2 t0,1,3 t0,2,3 t1,2,3 t0,1,4 t0,2,4 t1,2,4 t0,3,4 t1,3,4 t2,3,4 t0,1,5 t0,2,5 t1,2,5 t0,3,5 t1,3,5 t0,4,5 t0,1,6 t0,2,6 t0,3,6 t0,1,2,3 t0,1,2,4 t0,1,3,4 t0,2,3,4 t1,2,3,4 t0,1,2,5 t0,1,3,5 t0,2,3,5 t1,2,3,5 t0,1,4,5 t0,2,4,5 t1,2,4,5 t0,3,4,5 t0,1,2,6 t0,1,3,6 t0,2,3,6 t0,1,4,6 t0,2,4,6 t0,1,5,6 t0,1,2,3,4 t0,1,2,3,5 t0,1,2,4,5 t0,1,3,4,5 t0,2,3,4,5 t1,2,3,4,5 t0,1,2,3,6 t0,1,2,4,6 t0,1,3,4,6 t0,2,3,4,6 t0,1,2,5,6 t0,1,3,5,6 t0,1,2,3,4,5 t0,1,2,3,4,6 t0,1,2,3,5,6 t0,1,2,4,5,6 t0,1,2,3,4,5,6
Notes Edit ^ Klitzing, (x3o3o3x3o3o3o - spo) ^ Klitzing, (o3x3o3o3x3o3o - sibpo) ^ Klitzing, (x3x3o3x3o3o3o - patto) ^ Klitzing, (o3x3x3o3x3o3o - bipto) ^ Klitzing, (x3o3x3x3o3o3o - paro) ^ Klitzing, (x3x3x3x3o3o3o - gapo) ^ Klitzing, (o3x3x3x3x3o3o- gibpo) 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 Multi-dimensional Glossary
runcinated, simplexes, simplex, runcinated, simplex, biruncinated, simplexruncitruncated, simplex, biruncitruncated, simplex, runcicantellated, simplexbiruncicantellated, simplex, runcicantitruncated, simplex, biruncicantitruncated, simplexorthogonal, projecti. 7 simplex Runcinated 7 simplex Biruncinated 7 simplexRuncitruncated 7 simplex Biruncitruncated 7 simplex Runcicantellated 7 simplexBiruncicantellated 7 simplex Runcicantitruncated 7 simplex Biruncicantitruncated 7 simplexOrthogonal projections in A7 Coxeter planeIn seven dimensional geometry a runcinated 7 simplex is a convex uniform 7 polytope with 3rd order truncations runcination of the regular 7 simplex There are 8 unique runcinations of the 7 simplex with permutations of truncations and cantellations Contents 1 Runcinated 7 simplex 1 1 Alternate names 1 2 Coordinates 1 3 Images 2 Biruncinated 7 simplex 2 1 Alternate names 2 2 Coordinates 2 3 Images 3 Runcitruncated 7 simplex 3 1 Alternate names 3 2 Coordinates 3 3 Images 4 Biruncitruncated 7 simplex 4 1 Alternate names 4 2 Coordinates 4 3 Images 5 Runcicantellated 7 simplex 5 1 Alternate names 5 2 Coordinates 5 3 Images 6 Biruncicantellated 7 simplex 6 1 Alternate names 6 2 Coordinates 6 3 Images 7 Runcicantitruncated 7 simplex 7 1 Alternate names 7 2 Coordinates 7 3 Images 8 Biruncicantitruncated 7 simplex 8 1 Alternate names 8 2 Coordinates 8 3 Images 9 Related polytopes 10 Notes 11 References 12 External linksRuncinated 7 simplex EditRuncinated 7 simplexType uniform 7 polytopeSchlafli symbol t0 3 3 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdges 2100Vertices 280Vertex figureCoxeter group A7 36 order 40320Properties convexAlternate names Edit Small prismated octaexon acronym spo Jonathan Bowers 1 Coordinates Edit The vertices of the runcinated 7 simplex can be most simply positioned in 8 space as permutations of 0 0 0 0 1 1 1 2 This construction is based on facets of the runcinated 8 orthoplex Images Edit orthographic projections Ak Coxeter plane A7 A6 A5Graph nbsp nbsp nbsp Dihedral symmetry 8 7 6 Ak Coxeter plane A4 A3 A2Graph nbsp nbsp nbsp Dihedral symmetry 5 4 3 Biruncinated 7 simplex EditBiruncinated 7 simplexType uniform 7 polytopeSchlafli symbol t1 4 3 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdges 4200Vertices 560Vertex figureCoxeter group A7 36 order 40320Properties convexAlternate names Edit Small biprismated octaexon sibpo Jonathan Bowers 2 Coordinates Edit The vertices of the biruncinated 7 simplex can be most simply positioned in 8 space as permutations of 0 0 0 1 1 1 2 2 This construction is based on facets of the biruncinated 8 orthoplex Images Edit orthographic projections Ak Coxeter plane A7 A6 A5Graph nbsp nbsp nbsp Dihedral symmetry 8 7 6 Ak Coxeter plane A4 A3 A2Graph nbsp nbsp nbsp Dihedral symmetry 5 4 3 Runcitruncated 7 simplex Editruncitruncated 7 simplexType uniform 7 polytopeSchlafli symbol t0 1 3 3 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdges 4620Vertices 840Vertex figureCoxeter group A7 36 order 40320Properties convexAlternate names Edit Prismatotruncated octaexon acronym patto Jonathan Bowers 3 Coordinates Edit The vertices of the runcitruncated 7 simplex can be most simply positioned in 8 space as permutations of 0 0 0 0 1 1 2 3 This construction is based on facets of the runcitruncated 8 orthoplex Images Edit orthographic projections Ak Coxeter plane A7 A6 A5Graph nbsp nbsp nbsp Dihedral symmetry 8 7 6 Ak Coxeter plane A4 A3 A2Graph nbsp nbsp nbsp Dihedral symmetry 5 4 3 Biruncitruncated 7 simplex EditBiruncitruncated 7 simplexType uniform 7 polytopeSchlafli symbol t1 2 4 3 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdges 8400Vertices 1680Vertex figureCoxeter group A7 36 order 40320Properties convexAlternate names Edit Biprismatotruncated octaexon acronym bipto Jonathan Bowers 4 Coordinates Edit The vertices of the biruncitruncated 7 simplex can be most simply positioned in 8 space as permutations of 0 0 0 1 1 2 3 3 This construction is based on facets of the biruncitruncated 8 orthoplex Images Edit orthographic projections Ak Coxeter plane A7 A6 A5Graph nbsp nbsp nbsp Dihedral symmetry 8 7 6 Ak Coxeter plane A4 A3 A2Graph nbsp nbsp nbsp Dihedral symmetry 5 4 3 Runcicantellated 7 simplex Editruncicantellated 7 simplexType uniform 7 polytopeSchlafli symbol t0 2 3 3 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdges 3360Vertices 840Vertex figureCoxeter group A7 36 order 40320Properties convexAlternate names Edit Prismatorhombated octaexon acronym paro Jonathan Bowers 5 Coordinates Edit The vertices of the runcicantellated 7 simplex can be most simply positioned in 8 space as permutations of 0 0 0 0 1 2 2 3 This construction is based on facets of the runcicantellated 8 orthoplex Images Edit orthographic projections Ak Coxeter plane A7 A6 A5Graph nbsp nbsp nbsp Dihedral symmetry 8 7 6 Ak Coxeter plane A4 A3 A2Graph nbsp nbsp nbsp Dihedral symmetry 5 4 3 Biruncicantellated 7 simplex Editbiruncicantellated 7 simplexType uniform 7 polytopeSchlafli symbol t1 3 4 3 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter group A7 36 order 40320Properties convexAlternate names Edit Biprismatorhombated octaexon acronym bipro Jonathan Bowers Coordinates Edit The vertices of the biruncicantellated 7 simplex can be most simply positioned in 8 space as permutations of 0 0 0 1 2 2 3 3 This construction is based on facets of the biruncicantellated 8 orthoplex Images Edit orthographic projections Ak Coxeter plane A7 A6 A5Graph nbsp nbsp nbsp Dihedral symmetry 8 7 6 Ak Coxeter plane A4 A3 A2Graph nbsp nbsp nbsp Dihedral symmetry 5 4 3 Runcicantitruncated 7 simplex Editruncicantitruncated 7 simplexType uniform 7 polytopeSchlafli symbol t0 1 2 3 3 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdges 5880Vertices 1680Vertex figureCoxeter group A7 36 order 40320Properties convexAlternate names Edit Great prismated octaexon acronym gapo Jonathan Bowers 6 Coordinates Edit The vertices of the runcicantitruncated 7 simplex can be most simply positioned in 8 space as permutations of 0 0 0 0 1 2 3 4 This construction is based on facets of the runcicantitruncated 8 orthoplex Images Edit orthographic projections Ak Coxeter plane A7 A6 A5Graph nbsp nbsp nbsp Dihedral symmetry 8 7 6 Ak Coxeter plane A4 A3 A2Graph nbsp nbsp nbsp Dihedral symmetry 5 4 3 Biruncicantitruncated 7 simplex Editbiruncicantitruncated 7 simplexType uniform 7 polytopeSchlafli symbol t1 2 3 4 3 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdges 11760Vertices 3360Vertex figureCoxeter group A7 36 order 40320Properties convexAlternate names Edit Great biprismated octaexon acronym gibpo Jonathan Bowers 7 Coordinates Edit The vertices of the biruncicantitruncated 7 simplex can be most simply positioned in 8 space as permutations of 0 0 0 1 2 3 4 4 This construction is based on facets of the biruncicantitruncated 8 orthoplex Images Edit orthographic projections Ak Coxeter plane A7 A6 A5Graph nbsp nbsp nbsp Dihedral symmetry 8 7 6 Ak Coxeter plane A4 A3 A2Graph nbsp nbsp nbsp Dihedral symmetry 5 4 3 Related polytopes EditThese polytopes are among 71 uniform 7 polytopes with A7 symmetry A7 polytopes nbsp t0 nbsp t1 nbsp t2 nbsp t3 nbsp t0 1 nbsp t0 2 nbsp t1 2 nbsp t0 3 nbsp t1 3 nbsp t2 3 nbsp t0 4 nbsp t1 4 nbsp t2 4 nbsp t0 5 nbsp t1 5 nbsp t0 6 nbsp t0 1 2 nbsp t0 1 3 nbsp t0 2 3 nbsp t1 2 3 nbsp t0 1 4 nbsp t0 2 4 nbsp t1 2 4 nbsp t0 3 4 nbsp t1 3 4 nbsp t2 3 4 nbsp t0 1 5 nbsp t0 2 5 nbsp t1 2 5 nbsp t0 3 5 nbsp t1 3 5 nbsp t0 4 5 nbsp t0 1 6 nbsp t0 2 6 nbsp t0 3 6 nbsp t0 1 2 3 nbsp t0 1 2 4 nbsp t0 1 3 4 nbsp t0 2 3 4 nbsp t1 2 3 4 nbsp t0 1 2 5 nbsp t0 1 3 5 nbsp t0 2 3 5 nbsp t1 2 3 5 nbsp t0 1 4 5 nbsp t0 2 4 5 nbsp t1 2 4 5 nbsp t0 3 4 5 nbsp t0 1 2 6 nbsp t0 1 3 6 nbsp t0 2 3 6 nbsp t0 1 4 6 nbsp t0 2 4 6 nbsp t0 1 5 6 nbsp t0 1 2 3 4 nbsp t0 1 2 3 5 nbsp t0 1 2 4 5 nbsp t0 1 3 4 5 nbsp t0 2 3 4 5 nbsp t1 2 3 4 5 nbsp t0 1 2 3 6 nbsp t0 1 2 4 6 nbsp t0 1 3 4 6 nbsp t0 2 3 4 6 nbsp t0 1 2 5 6 nbsp t0 1 3 5 6 nbsp t0 1 2 3 4 5 nbsp t0 1 2 3 4 6 nbsp t0 1 2 3 5 6 nbsp t0 1 2 4 5 6 nbsp t0 1 2 3 4 5 6Notes Edit Klitzing x3o3o3x3o3o3o spo Klitzing o3x3o3o3x3o3o sibpo Klitzing x3x3o3x3o3o3o patto Klitzing o3x3x3o3x3o3o bipto Klitzing x3o3x3x3o3o3o paro Klitzing x3x3x3x3o3o3o gapo Klitzing o3x3x3x3x3o3o gibpo 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 x3o3o3x3o3o3o spo o3x3o3o3x3o3o sibpo x3x3o3x3o3o3o patto o3x3x3o3x3o3o bipto x3o3x3x3o3o3o paro x3x3x3x3o3o3o gapo o3x3x3x3x3o3o gibpoExternal links EditPolytopes of Various Dimensions 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 Runcinated 7 simplexes amp oldid 838576814 Biruncicantitruncated 7 simplex, wikipedia, wiki , book, books, library,
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