13-2 step prism

The 13-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 65 phyllic disphenoids of five kinds as cells, with 20 joining at each vertex. It can also be constructed as the 13-6 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$(1+2\cos\frac{2\pi}{13})\sec\frac{\pi}{26}\sqrt{\frac{1+\cos\frac{\pi}{13}-\cos\frac{2\pi}{13}+\sin\frac{\pi}{26}}{2}}$$ ≈ 1:2.16752.

Vertex coordinates
Coordinates for the vertices of a 13-2 step prism inscribed in a tridecagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 12. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to :$$\frac{1}{\sqrt{2\cos\frac{\pi}{13}-2\cos\frac{2\pi}{13}}}$$ ≈ 1:2.41846.
 * (a*sin(2πk/13), a*cos(2πk/13), b*sin(4πk/13), b*cos(4πk/13)),