8-cubic honeycomb


The 8-cubic honeycomb or octeractic honeycomb is the only regular space-filling tessellation in Euclidean 8-space.
It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space, and the tesseractic honeycomb of 4-space.
There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol. Another form has two alternating hypercube facets with Schläfli symbol. The lowest symmetry Wythoff construction has 256 types of facets around each vertex and a prismatic product Schläfli symbol 8.

Related honeycombs

The ,, Coxeter group generates 511 permutations of uniform tessellations, 271 with unique symmetry and 270 with unique geometry. The expanded 8-cubic honeycomb is geometrically identical to the 8-cubic honeycomb.
The 8-cubic honeycomb can be alternated into the 8-demicubic honeycomb, replacing the 8-cubes with 8-demicubes, and the alternated gaps are filled by 8-orthoplex facets.

Quadrirectified 8-cubic honeycomb

A quadrirectified 8-cubic honeycomb,, contains all trirectified 8-orthoplex facets and is the Voronoi tessellation of the D8* lattice. Facets can be identically colored from a doubled ×2, 4,36,4 symmetry, alternately colored from, symmetry, three colors from, symmetry, and 4 colors from, symmetry.