• Source: Quarter 5-cubic honeycomb

In five-dimensional Euclidean geometry, the 5.180.24.3/info/quarter" target="_blank">quarter 5-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 5-demicubic honeycomb, and a 5.180.24.3/info/quarter" target="_blank">quarter of the vertices of a 5-cube honeycomb. Its facets are 5-demicubes and runcinated 5-demicubes.




Related honeycombs


This honeycomb is one of 20 uniform honeycombs constructed by the







D
~




5




{\displaystyle {\tilde {D}}_{5}}

Coxeter group, all but 3 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 20 permutations are listed with its highest extended symmetry relation:




See also


Regular and uniform honeycombs in 5-space:

5-cube honeycomb
5-demicube honeycomb
5-simplex honeycomb
Truncated 5-simplex honeycomb
Omnitruncated 5-simplex honeycomb




Notes






References


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. "5D Euclidean tesselations#5D". x3o3o x3o3o *b3*e - spaquinoh

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