Square cupolic prism

The square cupolic prism, or squacupe, is a CRF segmentochoron (designated K-4.69 on Richard Klitzing's list). It consiss of 2 square cupolas, 4 triangular prisms, 1+4 cubes, and 1 octagonal prism.

As the name suggests, it is a prism based on the square cupola. As such, it is a segmentochoron between two square cupolas. It can also be viewed as a segmentochoron between an octagonal prism and a cube.

Two square cupolic prisms can be attached to opposite octagonal prismatic cells of the square-octagonal duoprism to produce a small rhombicuboctahedral prism.

Vertex coordinates
Coordinates of the vertices of a square cupolic prism of edge length 1 centered at the origin are given by:
 * $$\left(±\frac12,\,±\frac12,\,\frac{\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,0,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,0,\,±\frac12\right).$$