24-5 step prism

The 24-5 step prism is a convex isogonal polychoron, member of the step prism family. It has 144 phyllic disphenoids of three kinds as cells.

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)),