6-cubic honeycomb


The 6-cubic honeycomb or hexeractic honeycomb is the only regular space-filling tessellation in Euclidean 6-space.
It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space.

Constructions

There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol. Another form has two alternating 6-cube facets with Schläfli symbol. The lowest symmetry Wythoff construction has 64 types of facets around each vertex and a prismatic product Schläfli symbol 6.

Related honeycombs

The ,, Coxeter group generates 127 permutations of uniform tessellations, 71 with unique symmetry and 70 with unique geometry. The expanded 6-cubic honeycomb is geometrically identical to the 6-cubic honeycomb.
The 6-cubic honeycomb can be alternated into the 6-demicubic honeycomb, replacing the 6-cubes with 6-demicubes, and the alternated gaps are filled by 6-orthoplex facets.

Trirectified 6-cubic honeycomb

A trirectified 6-cubic honeycomb,, contains all birectified 6-orthoplex facets and is the Voronoi tessellation of the D6* lattice. Facets can be identically colored from a doubled ×2, 4,34,4 symmetry, alternately colored from, symmetry, three colors from, symmetry, and 4 colors from, symmetry.