In six-dimensional Euclidean geometry, the quarter 6-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 6-demicubic honeycomb, and a quarter of the vertices of a 6-cube honeycomb. Its facets are 6-demicubes, stericated 6-demicubes, and {3,3}×{3,3} duoprisms.
Related honeycombs This honeycomb is one of 41 uniform honeycombs constructed by the D ~ 6 {\displaystyle {\tilde {D}}_{6}} Coxeter group, all but 6 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 41 permutations are listed with its highest extended symmetry, and related B ~ 6 {\displaystyle {\tilde {B}}_{6}} and C ~ 6 {\displaystyle {\tilde {C}}_{6}} constructions:
See also Regular and uniform honeycombs in 5-space:
6-cube honeycomb 6-demicube honeycomb 6-simplex honeycomb Truncated 6-simplex honeycomb Omnitruncated 6-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] Archived 2016-07-11 at the Wayback Machine (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318 [2] Klitzing, Richard. "6D Euclidean tesselations#6D".
