Cube atop small rhombicuboctahedron

The cube atop small rhombicuboctahedron, or cubasirco, is a CRF segmentochoron (designated K-4.71 on Richard Klitzing's list). As the name suggests, it consists of a cube and a small rhombicuboctahedron as bases, connected by 8 tetrahedra, 12 triangular prisms, and 6 further cubes.

It is also sometimes referred to as a cubic cupola, as one generalization of the definition of a cupola is to have a polytope atop an expanded version.

A small disprismatotesseractihexadecachoron can be formed by attaching cube atop small rhombicuboctahedron segmentochora to the bases of the small rhombicuboctahedral prism.

Vertex coordinates
Coordinates for the vertices of a cube atop small rhombicuboctahedron of edge length 1 are given by: along with all permutations of the first three coordinates of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac{\sqrt2}{2}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,0\right).$$