In seven-dimensional Euclidean geometry, the quarter 7-cubic honeycomb is a uniform space-filling tessellation (or honeycomb).
[1] Its facets are 7-demicubes, pentellated 7-demicubes, and {31,1,1}×{3,3} duoprisms.
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
constructions: Regular and uniform honeycombs in 7-space: