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Quarter 8-cubic honeycomb

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quarter 8-cubic honeycomb
(No image)
Type Uniform 8-honeycomb
Family Quarter hypercubic honeycomb
Schläfli symbol q{4,3,3,3,3,3,3,4}
Coxeter diagram =
7-face type h{4,36},
h6{4,36},
{3,3}×{32,1,1} duoprism
{31,1,1}×{31,1,1} duoprism
Vertex figure
Coxeter group ×2 = [[31,1,3,3,3,3,31,1]]
Dual
Properties vertex-transitive

In seven-dimensional Euclidean geometry, the quarter 8-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 8-demicubic honeycomb, and a quarter of the vertices of a 8-cube honeycomb.[1] Its facets are 8-demicubes h{4,36}, pentic 8-cubes h6{4,36}, {3,3}×{32,1,1} and {31,1,1}×{31,1,1} duoprisms.

See also

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Regular and uniform honeycombs in 8-space:

Notes

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  1. ^ Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318

References

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  • 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 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318 [2]
  • Klitzing, Richard. "7D Euclidean tesselations#7D".
Space Family / /
E2 Uniform tiling 0[3] δ3 3 3 Hexagonal
E3 Uniform convex honeycomb 0[4] δ4 4 4
E4 Uniform 4-honeycomb 0[5] δ5 5 5 24-cell honeycomb
E5 Uniform 5-honeycomb 0[6] δ6 6 6
E6 Uniform 6-honeycomb 0[7] δ7 7 7 222
E7 Uniform 7-honeycomb 0[8] δ8 8 8 133331
E8 Uniform 8-honeycomb 0[9] δ9 9 9 152251521
E9 Uniform 9-honeycomb 0[10] δ10 10 10
E10 Uniform 10-honeycomb 0[11] δ11 11 11
En-1 Uniform (n-1)-honeycomb 0[n] δn n n 1k22k1k21