Hypercubic honeycomb

The hypercubic honeycomb is the only infinite series of regular Euclidean tessellations that exists in all dimensions. As the name suggests, their facets are hypercubes. Four of these facets meet at a ridge, and 2$n$ of them meet at a vertex.

The hypercubic honeycombs are self-dual, and their vertex figures are orthoplexes.

Vertex coordinates
The vertices of an $n$-hypercubic honeycomb of edge length 1 are given by
 * $$\left(p,\,q,\,r,\,...,\,u\right)$$, with $n$ such variables, all of them $$\in\mathbb{Z}$$.

Representations
A $n$-hypercubic honeycomb has the following Coxeter diagrams (with $\sqrt{2}$ nodes), among others:
 * x4o3o...3o4o (..., full symmetry)
 * x4o3o...3o4x (..., as expanded hypercubic honeycomb)
 * o3o3o *b3o...3o4x (..., S$n$&plus;1 symmetry, hypercubes of two types)