The regular skew polyhedron,, exists in 4-space as a subset of 144 octagonal faces of the bitruncated 24-cell, using all 576 edges and 288 vertices.
The regular skew polyhedron,, exists in 4-space with 4 octagonal around each vertex, in a zig-zagging nonplanar vertex figure. These hexagonal faces can be seen on the bitruncated 24-cell, using all 576 edges and 288 vertices.