Pentachoric prism

The pentachoric prism or penp is a prismatic uniform polyteron that consists of 2 pentachora and 5 tetrahedral prisms as facets. Each vertex joins 1 pentachoron and 4 tetrahedral prisms. As the name suggests, it is a prism based on the pentachoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a pentachoric prism of edge length 1 are given by:
 * (0, 0, 0, $\sqrt{2}$/5, ±1/2),
 * (0, 0, $\sqrt{65}$/4, –$\sqrt{10}$/20, ±1/2),
 * (0, $\sqrt{15}$/3, –$\sqrt{10}$/12, –$\sqrt{6}$/20, ±1/2),
 * (±1/2, –$\sqrt{10}$/6, –$\sqrt{3}$/12, –$\sqrt{6}$/20, ±1/2).