Pentachoric prism

The pentachoric prism or penp is a prismatic uniform polyteron that consists of 2 tetrahedra and 4 triangular prisms.

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, $\sqrt{6}$/3, –$\sqrt{10}$/12, –$\sqrt{3}$/20, ±1/2),
 * (±1/2, –$\sqrt{6}$/6, –$\sqrt{10}$/12, –$\sqrt{3}$/20, ±1/2).