• Source: Omnitruncated 8-simplex honeycomb

      • In eight-dimensional Euclidean geometry, the omnitruncated 8-simplex honeycomb is a space-filling tessellation (or honeycomb). It is composed entirely of omnitruncated 8-simplex facets.
      The facets of all omnitruncated simplectic honeycombs are called permutahedra and can be positioned in n+1 space with integral coordinates, permutations of the whole numbers (0,1,..,n).


      A*8 lattice


      The A*8 lattice (also called A98) is the union of nine A8 lattices, and has the vertex arrangement of the dual honeycomb to the omnitruncated 8-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 8-simplex

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      = dual of .


      Related polytopes and honeycombs


      This honeycomb is one of 45 unique uniform honeycombs constructed by
      the







      A
      ~




      8




      {\displaystyle {\tilde {A}}_{8}}

      Coxeter group. The symmetry can be multiplied by the ring symmetry of the Coxeter diagrams:


      See also


      Regular and uniform honeycombs in 8-space:

      8-cubic honeycomb
      8-demicubic honeycomb
      8-simplex honeycomb
      Truncated 8-simplex honeycomb
      521 honeycomb
      251 honeycomb
      152 honeycomb


      Notes




      References


      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]

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