Retrograde square cupola

The retrograde square cupola or rasquacu, also called crossed square cupola, consists of 4 triangles, 1+4 squares, and 1 octagram. It can be seen as a cupola based on a retrograde square.

It is the x4/3o-square-first cap of the quasirhombicuboctahedron, which can be formed from 2 retrograde square cupolas and an octagrammic prism.

Vertex coordinates
A square cupola of edge length 1 has vertices given by the following coordinates:


 * $$\left(±\frac12,\,±\frac12,\,\frac{\sqrt2}{2}\right),$$
 * $$\left(±\frac{\sqrt2-1}{2},\,±\frac12,\,0\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt2-1}{2},\,0\right).$$

These can be obtained from placing a square and octagram in parallel planes.

Representations
A retrograde square cupola has the following Coxeter diagrams:


 * ox4/3xx&#x
 * so8/3ox&#x