Cube atop cuboctahedron

Cube atop cuboctahedron, or cubaco, is a CRF segmentochoron (designated K-4.35 on Richard Klitzing's list). As the name suggests, it consists of a cube and a cuboctahedron as bases, connected by 8 tetrahedra and 6 square antiprisms.

Vertex coordinates
The vertices of a cube atop cuboctahedron segmentochoron of edge length 1 are given by:
 * $$\left(±\frac{1}{2},\,±\frac{1}{2},\,±\frac{1}{2},\,\frac{\sqrt{4\sqrt{2}-3}}{2}\right),$$
 * $$\left(±\frac{\sqrt{2}}{2},\,±\frac{\sqrt{2}}{2},\,0,\,0\right)$$ and all permutations of first three coordinates.