^Deza, Michael; Shtogrin, Mikhael (1998). "Embedding the graphs of regular tilings and star-honeycombs into the graphs of hypercubes and cubic lattices". Advanced Studies in Pure Mathematics. Arrangements – Tokyo 1998: 77. doi:10.2969/aspm/02710073. ISBN978-4-931469-77-8. Retrieved 4 April 2020.
Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN0-486-61480-8, p.296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p.296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
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, ISBN978-0-471-01003-6[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]
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN978-1-56881-220-5 (Chapter 26. pp. 409: Hemicubes: 1n1)
demicube, demidekeract, petrie, polygon, projection, type, uniform, polytope, family, demihypercube, coxeter, symbol, schläfli, symbol, coxeter, diagram, faces, faces, 5300, 5120, faces, 24000, 23040, faces, 64800, 3360, 61440, faces, 115584, 8064, 107520, fac. Demidekeract 10 demicube Petrie polygon projection Type Uniform 10 polytope Family demihypercube Coxeter symbol 171 Schlafli symbol 31 7 1 h 4 38 s 21 1 1 1 1 1 1 1 1 Coxeter diagram 9 faces 532 20 31 6 1 512 38 8 faces 5300 180 31 5 1 5120 37 7 faces 24000 960 31 4 1 23040 36 6 faces 64800 3360 31 3 1 61440 35 5 faces 115584 8064 31 2 1 107520 34 4 faces 142464 13440 31 1 1 129024 33 Cells 122880 15360 31 0 1 107520 3 3 Faces 61440 3 Edges 11520 Vertices 512 Vertex figure Rectified 9 simplex Symmetry group D10 37 1 1 1 4 38 29 Dual Properties convex In geometry a 10 demicube or demidekeract is a uniform 10 polytope constructed from the 10 cube with alternated vertices removed It is part of a dimensionally infinite family of uniform polytopes called demihypercubes E L Elte identified it in 1912 as a semiregular polytope labeling it as HM10 for a ten dimensional half measure polytope Coxeter named this polytope as 171 from its Coxeter diagram with a ring on one of the 1 length branches and Schlafli symbol 3 3 3 3 3 3 3 3 3 displaystyle left 3 begin array l 3 3 3 3 3 3 3 3 end array right or 3 37 1 Contents 1 Cartesian coordinates 2 Images 3 Related polytopes 4 References 5 External linksCartesian coordinates editCartesian coordinates for the vertices of a demidekeract centered at the origin are alternate halves of the dekeract 1 1 1 1 1 1 1 1 1 1 with an odd number of plus signs Images edit nbsp B10 coxeter plane nbsp D10 coxeter plane Vertices are colored by multiplicity red orange yellow green 1 2 4 8 Related polytopes editA regular dodecahedron can be embedded as a regular skew polyhedron within the vertices in the 10 demicube posessing the same symmetries as the 3 dimensional dodecahedron 1 References edit Deza Michael Shtogrin Mikhael 1998 Embedding the graphs of regular tilings and star honeycombs into the graphs of hypercubes and cubic lattices Advanced Studies in Pure Mathematics Arrangements Tokyo 1998 77 doi 10 2969 aspm 02710073 ISBN 978 4 931469 77 8 Retrieved 4 April 2020 H S M Coxeter Coxeter Regular Polytopes 3rd edition 1973 Dover edition ISBN 0 486 61480 8 p 296 Table I iii Regular Polytopes three regular polytopes in n dimensions n 5 H S M Coxeter Regular Polytopes 3rd Edition Dover New York 1973 p 296 Table I iii Regular Polytopes three regular polytopes in n dimensions n 5 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 John H Conway Heidi Burgiel Chaim Goodman Strauss The Symmetries of Things 2008 ISBN 978 1 56881 220 5 Chapter 26 pp 409 Hemicubes 1n1 Norman Johnson Uniform Polytopes Manuscript 1991 N W Johnson The Theory of Uniform Polytopes and Honeycombs Ph D 1966 Klitzing Richard 10D uniform polytopes polyxenna x3o3o b3o3o3o3o3o3o3o hede External links editOlshevsky George Demienneract Glossary for Hyperspace Archived from the original on 4 February 2007 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 10 demicube amp oldid 1213189058, wikipedia, wiki, book, books, library,
