Small rhombicuboctahedron atop truncated octahedron

Small rhombicuboctahedron atop truncated octahedron, or sircoatoe, is a CRF segmentochoron (designated K-4.75 on Richard Klitzing's list). As the name suggests, it consists of a small rhombicuboctahedron and a truncated octahedron as bases, connected by 12 triangular prisms, 6 square antiprisms, and 8 triangular cupolas.

Vertex coordinates
The vertices of a small rhombicuboctahedron atop truncated octahedron segmentochoron of edge length 1 are given by:
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,\frac{\sqrt{4\sqrt2-3}}{2}\right)$$ and all permutations of the first three coordinates,
 * $$\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,0,\,0\right)$$ and all permutations of the first three coordinates.