50-7 step prism

The 50-7 step prism is a convex isogonal polychoron, member of the step prism family. It has 50 tetragonal disphenoids and 500 phyllic disphenoids of five kinds as cells. 4 tetragonal and 40 phylic disphenoids join at each vertex.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2+\cos\frac{3\pi}{25}-2\cos\frac{4\pi}{25}}{2-\cos\frac{\pi}{25}-\sin\frac{11\pi}{50}}}$$ ≈ 1:2.35436.

Vertex coordinates
Coordinates for the vertices of a 50-7 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 49.
 * (sin(πk/25), cos(πk/25), sin(7πk/25), cos(7πk/25)),