- Omnitruncated 5-simplex honeycomb
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Omnitruncated 5-simplex honeycomb (No image) Type Uniform honeycomb Family Omnitruncated simplectic honeycomb Schläfli symbol t0,1,2,3,4,5{3[6]} Coxeter–Dynkin diagrams 
5-face types t0,1,2,3,4{3,3,3,3} 
4-face types t0,1,2,3{3,3,3} 
{}×t0,1,2{3,3}
{6}×{6}
Cell types t0,1,2{3,3} 
{4,3}
{}x{6}
Face types {4}
{6}Vertex figure 
Irr. 5-simplexCoxeter groups 
, [3[6]]Properties vertex-transitive In five-dimensional Euclidean geometry, the omnitruncated 5-simplex honeycomb or omnitruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed entirely of omnitruncated 5-simplex facets.
Contents
Related polytopes and honeycombs
This honeycomb is one of 12 unique uniform honycombs constructed by the
Coxeter group. The Coxeter–Dynkin diagrams of the other 11 are: 
, 
, 
, , , , , , , , .Projection by folding
The omnitruncated 5-simplex honeycomb can be projected into the 3-dimensional omnitruncated cubic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same 3-space vertex arrangement:
See also
- Regular and uniform honeycombs in 5-space:
- Penteractic honeycomb
- Demipenteractic honeycomb
- 5-simplex honeycomb
- Truncated 5-simplex 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]
This geometry-related article is a stub. You can help Wikipedia by expanding it. - Regular and uniform honeycombs in 5-space:
