Mucube

The mucube is one of the three regular skew apeirohedra in euclidean 3-space (or Petrie-Coxeter polyhedra).

It's an infinite polyhedron that consists solely of squares. It is effectively composed of individual units that are equivalent to a cube with two opposite sides removed.

It is based on the cubic honeycomb. Its faces are a subset of the faces of the cubic honeycomb, but with some removed (square holes) such that each set of coplanar faces turns into a checkerboard pattern.

Vertex coordinates
Assuming an edge length of 1, each vertex is of the form (n, m, o) where n, m, and o are integers.

Derivatives

 * Dual: Muoctahedron
 * Petrial: Petrial mucube
 * Halved mucube