Quarter 7 cubic honeycomb - Alchetron, the free social encyclopedia

In seven-dimensional Euclidean geometry, the quarter 7-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 7-demicubic honeycomb, and a quarter of the vertices of a 7-cube honeycomb. Its facets are 7-demicubes, pentellated 7-demicubes, and {3^1,1,1}×{3,3} duoprisms.

This honeycomb is one of 77 uniform honycombs constructed by the D ~ 7 Coxeter group, all but 10 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 77 permutations are listed with its highest extended symmetry, and related B ~ 7 and C ~ 7 constructions:

References

Quarter 7-cubic honeycomb Wikipedia

(Text) CC BY-SA

Related honeycombs

References