Octahedron atop small rhombicuboctahedron

Octahedron atop small rhombicuboctahedron, or octasirco, is a CRF segmentochoron (designated K-4.107 on Richard Klitzing's list). As the name suggests, it consists of an octahedron and a small rhombicuboctahedron as bases, connected by 8+12 triangular prisms, and 6 square pyramids.

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

It can be obtained as a segment of the small prismatotetracontoctachoron, which can be constructed by attaching 8 of these segmentochora to the small rhombicuboctahedral cells of the small rhombated tesseract.

Vertex coordinates
The vertices of an octahedron atop small rhombicuboctahedron segmentochoron of edge length 1 are given by:


 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,\frac12\right)$$ and all permutations of first three coordinates
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,0\right)$$ and all permutations of first three coordinates