41-9 step prism

The 41-9 step prism is a convex isogonal polychoron, member of the step prism family. It has 41 tetragonal disphenoids and 246 phyllic disphenoids of three kinds as cells. 4 tetragonal and 24 phyllic disphenoids join at each vertex. It is also the 41-32 step prism.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{4-2\cos\frac{4\pi}{41}+2\cos\frac{5\pi}{41}}{4-2\cos\frac{8\pi}{41}-2\cos\frac{10\pi}{41}}}$$ ≈ 1:2.06812.

Vertex coordinates
Coordinates for the vertices of a 41-9 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 40.
 * (sin(2πk/41), cos(2πk/41), sin(18πk/41), cos(18πk/41)),