Petrial mucube

The  is a regular skew apeirohedron in 3 dimensional Euclidean space. It is the Petrie dual of the mucube.

Vertex coordinates
It's vertex coordinates are the same as the mucube. For a Petrial mucube of unit side length its vertices take on the coordinates where $N$, $3M&times;N$, $M&times;N$ are any three integers.
 * $$(i, j, k)$$,