Square pyramidal prism

The square pyramidal prism is a CRF segmentochoron (designated K-4.12 on Richard Klitzing's list). Its cells are 2 square pyramids connected by 1 cube and 4 triangular prisms.

As the name suggests, it is a prism based on the square pyramid. As such, it is a segmentochoron between two square pyramids. It can also be viewed as a segmentochoron between a cube and a dyad.

Vertex coordinates
The coordinates of the vertices of a square pyramidal prism of edge length 1 centered at the origin are given by:
 * (±1/2, ±1/2, 0, ±1/2),
 * (0, 0, $\sqrt{3}$/2, ±1/2).