Great cubihexadecadisoctachoron

The great cubihexadecadisoctachoron, or gichado, is a nonconvex uniform polychoron that consists of 24 cubes, 16 truncated tetrahedra, 8 great cubicuboctahedra, and 8 quasitruncated cuboctahedra. 1 cube, 1 truncated tetrahedron, 1 great cubicuboctahedron, and 2 quasitruncated cuboctahedra join at each vertex.

The great cubihexadecadisoctachoron contains the vertices of a quasitruncated cuboctahedral prism.

Vertex coordinates
The vertices of a great cubihexadecadisoctachoron of edge length 1 are given by all permutations of:
 * $$\left(±\frac{2\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12\right).$$