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:
 * (±1/2, ±1/2, ±1/2, $\sqrt{2}$/2)
 * (±$\sqrt{2}$/2, ±$\sqrt{(16+6√2)/23}$/2, 0, 0) and all permuations of first three coordinates