Structure edit Related polytopes and honeycombs edit This honeycomb is one of 45 unique uniform honeycombs [1] A ~ 8 {\displaystyle {\tilde {A}}_{8}} Coxeter group . The symmetry can be multiplied by the ring symmetry of the Coxeter diagrams :
A8 honeycombs Enneagon Symmetry Extended Extended Honeycombs a1 [3[9] ] A ~ 8 {\displaystyle {\tilde {A}}_{8}}
i2 [[3[9] ]] A ~ 8 {\displaystyle {\tilde {A}}_{8}} 1 2
i6 [3[3[9] ]] A ~ 8 {\displaystyle {\tilde {A}}_{8}} r18 [9[3[9] ]] A ~ 8 {\displaystyle {\tilde {A}}_{8}} 3
See also edit Regular and uniform honeycombs in 8-space:
Notes edit References edit Norman Johnson Uniform Polytopes , Manuscript (1991)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] (1.9 Uniform space-fillings) (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III , [Math. Zeit. 200 (1988) 3-45]
cyclotruncated, simplex, honeycomb, image, type, uniform, honeycombfamily, cyclotruncated, simplectic, honeycombschläfli, symbol, coxeter, diagram8, face, types, vertex, figure, elongated, simplex, antiprismsymmetry, displaystyle, tilde, properties, vertex, tr. Cyclotruncated 8 simplex honeycomb No image Type Uniform honeycombFamily Cyclotruncated simplectic honeycombSchlafli symbol t0 1 3 9 Coxeter diagram8 face types 37 t0 1 37 t1 2 37 t2 3 37 t3 4 37 Vertex figure Elongated 7 simplex antiprismSymmetry A 8 displaystyle tilde A 8 2 3 9 Properties vertex transitiveIn eight dimensional Euclidean geometry the cyclotruncated 8 simplex honeycomb is a space filling tessellation or honeycomb The tessellation fills space by 8 simplex truncated 8 simplex bitruncated 8 simplex tritruncated 8 simplex and quadritruncated 8 simplex facets These facet types occur in proportions of 2 2 2 2 1 respectively in the whole honeycomb Contents 1 Structure 2 Related polytopes and honeycombs 3 See also 4 Notes 5 ReferencesStructure editIt can be constructed by nine sets of parallel hyperplanes that divide space The hyperplane intersections generate cyclotruncated 7 simplex honeycomb divisions on each hyperplane Related polytopes and honeycombs editThis honeycomb is one of 45 unique uniform honeycombs 1 constructed by the A 8 displaystyle tilde A 8 nbsp Coxeter group The symmetry can be multiplied by the ring symmetry of the Coxeter diagrams A8 honeycombsEnneagonsymmetry Symmetry Extendeddiagram Extendedgroup Honeycombsa1 3 9 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp A 8 displaystyle tilde A 8 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 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 i2 3 9 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp A 8 displaystyle tilde A 8 nbsp 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 1 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 2 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 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 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 i6 3 3 9 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp A 8 displaystyle tilde A 8 nbsp 6 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp r18 9 3 9 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp A 8 displaystyle tilde A 8 nbsp 18 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 3See also editRegular and uniform honeycombs in 8 space 8 cubic honeycomb 8 demicubic honeycomb 8 simplex honeycomb Omnitruncated 8 simplex honeycomb 521 honeycomb 251 honeycomb 152 honeycombNotes edit Weisstein Eric W Necklace MathWorld OEIS sequence A000029 46 1 cases skipping one with zero marksReferences editNorman Johnson Uniform Polytopes Manuscript 1991 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 1 9 Uniform space fillings Paper 24 H S M Coxeter Regular and Semi Regular Polytopes III Math Zeit 200 1988 3 45 vteFundamental convex regular and uniform honeycombs in dimensions 2 9Space Family A n 1 displaystyle tilde A n 1 nbsp C n 1 displaystyle tilde C n 1 nbsp B n 1 displaystyle tilde B n 1 nbsp D n 1 displaystyle tilde D n 1 nbsp G 2 displaystyle tilde G 2 nbsp F 4 displaystyle tilde F 4 nbsp E n 1 displaystyle tilde E n 1 nbsp E2 Uniform tiling 3 3 d3 hd3 qd3 HexagonalE3 Uniform convex honeycomb 3 4 d4 hd4 qd4E4 Uniform 4 honeycomb 3 5 d5 hd5 qd5 24 cell honeycombE5 Uniform 5 honeycomb 3 6 d6 hd6 qd6E6 Uniform 6 honeycomb 3 7 d7 hd7 qd7 222E7 Uniform 7 honeycomb 3 8 d8 hd8 qd8 133 331E8 Uniform 8 honeycomb 3 9 d9 hd9 qd9 152 251 521E9 Uniform 9 honeycomb 3 10 d10 hd10 qd10E10 Uniform 10 honeycomb 3 11 d11 hd11 qd11En 1 Uniform n 1 honeycomb 3 n dn hdn qdn 1k2 2k1 k21 Retrieved from https en wikipedia org w index php title Cyclotruncated 8 simplex honeycomb amp oldid 1204991832, wikipedia, wiki , book, books, library,
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