Mucubic honeycomb

The petroid cubic honeycomb or mucubic honeycomb is a regular skew polychoron consisting of 4 mucubes. It shares its faces, edges, and vertices with the cubic honeycomb, and it has a petrial octahedron vertex figure. Its name comes from the fact that its vertex figure is the Petrie dual of the cubic honeycomb's vertex figure.

Vertex coordinates
The vertex coordinates of the petroid cubic honeycomb are the same as that of its regiment colonel, the cubic honeycomb.