• Source: Cyclotruncated 7-simplex honeycomb

    • In seven-dimensional Euclidean geometry, the cyclotruncated 7-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 7-simplex, truncated 7-simplex, bitruncated 7-simplex, and tritruncated 7-simplex facets. These facet types occur in proportions of 1:1:1:1 respectively in the whole honeycomb.


    Structure


    It can be constructed by eight sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 6-simplex honeycomb divisions on each hyperplane.


    Related polytopes and honeycombs


    This honeycomb is one of 29 unique uniform honeycombs constructed by
    the







    A
    ~




    7




    {\displaystyle {\tilde {A}}_{7}}

    Coxeter group, grouped by their extended symmetry of rings within the regular octagon diagram:


    See also


    Regular and uniform honeycombs in 7-space:

    7-cubic honeycomb
    7-demicubic honeycomb
    7-simplex honeycomb
    Omnitruncated 7-simplex honeycomb
    331 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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