• Source: Cyclotruncated 8-simplex honeycomb

    • In 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.


    Structure


    It 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


    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
    Omnitruncated 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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