37-6 step prism

The 37-6 step prism is a convex isogonal polychoron, member of the step prism family. It has 37 tetragonal disphenoids and 296 phyllic disphenoids of four kinds as cells. 4 tetragonal and 32 phyllic disphenoids join at each vertex. It is also the 37-31 step prism.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{4+2\cos\frac{\pi}{37}-2\cos\frac{6\pi}{37}}{4-2\cos\frac{2\pi}{37}-2\sin\frac{13\pi}{74}}}$$ ≈ 1:2.08153.

Vertex coordinates
Coordinates for the vertices of a 37-6 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 36.
 * (sin(2πk/37), cos(2πk/37), sin(12πk/37), cos(12πk/37)),