Discrete time and continuous time

Truncated 8-simplex honeycomb
(No image)
Type	Uniform honeycomb
Family	Truncated simplectic honeycomb
Schläfli symbol	t0,1{3[9]}
Coxeter–Dynkin diagrams	Template:CDD
8-face types	{37} , t0,1{37} t1,2{37} , t2,3{37} t3,4{37}
Vertex figure	Elongated 7-simplex antiprism
Symmetry	${\tilde {A}}_{8}$×2, [[3[9]]]
Properties	vertex-transitive

In eight-dimensional Euclidean geometry, the truncated 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.

It can be constructed by nine sets of parallel hyperplanes that divide space. The hyperplane intersections generate truncated 7-simplex honeycomb divisions on each hyperplane.

Related polytopes and honeycombs

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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

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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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