Cuboctahedron atop small rhombicuboctahedron

The cuboctahedron atop small rhombicuboctahedron, or coasirco, is a CRF segmentochoron (designated K-4.61 on Richard Klitzing's list). As the name suggests, it consists of a cuboctahedron and a small rhombicuboctahedron as bases, connected by 8 octahedra, 12 square pyramids, and 6 square antiprisms.

Vertex coordinates
The vertices of a cuboctahedron atop small rhombicuboctahedron segmentochoron of edge length 1 are given by:
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,\frac{\sqrt{2\sqrt2-1}}{2}\right)$$ and all permutations of first three coordinates
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,0\right)$$ and all permutations of first three coordinates