Omnitruncated 5-cell honeycomb

Omnitruncated 4-simplex honeycomb
(No image)
Type	Uniform honeycomb
Family	Omnitruncated simplectic honeycomb
Schläfli symbol	t0,1,2,3,4{3[5]}
Coxeter–Dynkin diagrams
4-face types	t0,1,2,3{3,3,3}
Cell types	t0,1,2{3,3} {6}x{}
Face types	{4} {6}
Vertex figure	Irr. 5-cell
Coxeter groups	${\tilde{A}}_4$, [3[5]]
Properties	vertex-transitive, cell-transitive

In four-dimensional Euclidean geometry, the omnitruncated 4-simplex honeycomb or omnitruncated 5-cell honeycomb is a space-filling tessellation honeycomb. It is composed entirely of omnitruncated 5-cell (omnitruncated 4-simplex) facets.

Coxeter calls this Hinton's honeycomb after C. H. Hinton, who described it in his book The Fourth Dimension in 1906.^[1]

Alernate names

• Omnitruncated cyclopentachoric tetracomb
• Great-prismatodecachoric tetracomb

Related polytopes and honeycombs

This honeycomb is one of 7 unique uniform honycombs constructed by the ${\tilde{A}}_4$ Coxeter group. The Coxeter–Dynkin diagrams of the other six are: , , , , ,.

See also

• Regular and uniform honeycombs in 4-space:
  • tesseractic honeycomb
  • 16-cell honeycomb
  • 24-cell honeycomb
  • Truncated 24-cell honeycomb
  • Snub 24-cell honeycomb
  • 5-cell honeycomb
  • Truncated 5-cell honeycomb

Notes

1. ^ The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8 (The classification of Zonohededra, page 73)

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]
• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 140
• Richard Klitzing, 4D, Euclidean tesselations, x3x3x3x3x3*a - otcypit - 140