Cubic honeycomb

The cubic honeycomb, or chon, is the only regular honeycomb or tesselation of 3D Euclidean space. 8 cubes join at each vertex of this honeycomb. It is also the 3D hypercubic honeycomb.

Vertex coordinates
The vertices of a cubic honeycomb of edge length 1 are given by


 * $$(i,j,k)$$ in which $$\{i,j,k\}\in\mathbb{Z}$$.

Representations
A cubic honeycomb has the following Coxeter diagrams:


 * x4o3o4o (regular)
 * x4o3o4x (as expanded cubic honecyomb)
 * o3o3o *b4x (S4 symmetry)
 * x∞o x4o4o (various square prismatic honeycombs)
 * x∞o o4x4o
 * x∞o x4o4x
 * x∞x x4o4o
 * x∞x o4x4o
 * x∞x x4o4x
 * x∞o x∞o x∞o (various apeirogonal triprismatic honeycomb)
 * x∞x x∞o x∞o
 * x∞x x∞x x∞o
 * x∞x x∞x x∞x
 * qo3oo3oq3oo3*a&#zx (as hull of two alternate tetrahedral-octahedral honeycombs)