Cyclotruncated 5-simplex honeycomb

Cyclotruncated 5-simplex honeycomb
(No image)
Type	Uniform honeycomb
Family	Cyclotruncated simplectic honeycomb
Schläfli symbol	t0,1{3[6]}
Coxeter diagram	Template:CDD or Template:CDD
5-face types	{3,3,3,3} t{3,3,3,3} 2t{3,3,3,3}
4-face types	{3,3,3} t{3,3,3}
Cell types	{3,3} t{3,3}
Face types	{3} t{3}
Vertex figure	Elongated 5-cell antiprism
Coxeter groups	${\tilde{A}}_5$×22, Template:Brackets
Properties	vertex-transitive

In five-dimensional Euclidean geometry, the cyclotruncated 5-simplex honeycomb or cyclotruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed of 5-simplex, truncated 5-simplex, and bitruncated 5-simplex facets in a ratio of 1:1:1.

Structure

Its vertex figure is an elongated 5-cell antiprism, two parallel 5-cells in dual configurations, connected by 10 tetrahedral pyramids (elongated 5-cells) from the cell of one side to a point on the other. The vertex figure has 8 vertices and 12 5-cells.

It can be constructed as six sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 5-cell honeycomb divisions on each hyperplane.

See also

Regular and uniform honeycombs in 5-space:

• 5-cubic honeycomb
• 5-demicubic honeycomb
• 5-simplex honeycomb
• Omnitruncated 5-simplex honeycomb

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, Template:ISBN [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]