It represents the Minkowski sum of a cube, a truncated octahedron, and a rhombic dodecahedron.
[1] It has 148 faces (8 triangles, 126 squares, 8 hexagons, and 6 octagons), 312 edges, and 144 vertices.
Without the triangular prisms, the toroidal polyhedron becomes a truncated cuboctahedron.
The truncated cuboctahedron is similar, with all regular faces, and 4.6.8 vertex figure.
The triangle and squares of the rhombicuboctahedron can be independently rectified or truncated, creating four permutations of polyhedra.