7-cubic honeycomb


The 7-cubic honeycomb or hepteractic honeycomb is the only regular space-filling tessellation in Euclidean 7-space.
It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space.
There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol. Another form has two alternating 7-cube facets with Schläfli symbol. The lowest symmetry Wythoff construction has 128 types of facets around each vertex and a prismatic product Schläfli symbol 7.

Related honeycombs

The ,, Coxeter group generates 255 permutations of uniform tessellations, 135 with unique symmetry and 134 with unique geometry. The expanded 7-cubic honeycomb is geometrically identical to the 7-cubic honeycomb.
The 7-cubic honeycomb can be alternated into the 7-demicubic honeycomb, replacing the 7-cubes with 7-demicubes, and the alternated gaps are filled by 7-orthoplex facets.

Quadritruncated 7-cubic honeycomb

A quadritruncated 7-cubic honeycomb,, contains all tritruncated 7-orthoplex facets and is the Voronoi tessellation of the D7* lattice. Facets can be identically colored from a doubled ×2, 4,35,4 symmetry, alternately colored from, symmetry, three colors from, symmetry, and 4 colors from, symmetry.