The 6-cubic honeycomb or hexeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 6-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 {4,3<sup>4</sup>,4}. Another form has two alternating 6-cube facets (like a checkerboard) with Schläfli symbol {4,3<sup>3</sup>,3<sup>1,1</sup>}. The lowest symmetry Wythoff construction has 64 types of facets around each vertex and a prismatic product Schläfli symbol {âÂÂ}<sup>(6)</sup>.
The [4,3<sup>4</sup>,4], , 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.
A trirectified 6-cubic honeycomb, , contains all birectified 6-orthoplex facets and is the Voronoi tessellation of the D<sub>6</sub><sup>*</sup> lattice. Facets can be identically colored from a doubled ÃÂ2, <nowiki>[</nowiki>4,3<sup>4</sup>,4] symmetry, alternately colored from , [4,3<sup>4</sup>,4] symmetry, three colors from , [4,3<sup>3</sup>,3<sup>1,1</sup>] symmetry, and 4 colors from , [3<sup>1,1</sup>,3,3,3<sup>1,1</sup>] symmetry.