24-5 step prism

The 24-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 144 phyllic disphenoids of three kinds as cells, with 12 cells joining at each vertex.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{40+10\sqrt6}}{5}$$ ≈ 1:1.60617.

Vertex coordinates
Coordinates for the vertices of a 24-5 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 23.
 * (sin(πk/12), cos(πk/12), sin(5πk/12), cos(5πk/12)),