11-3 step prism

The 11-3 step prism is a convex isogonal polychoron and a member of the step prism family. It has 33 phyllic disphenoids of three kinds as cells, with 12 joining at each vertex. It can also be constructed as the 11-4 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{14\cos\frac{\pi}{11}-4\sin\frac{\pi}{22}-1}{10\cos\frac{\pi}{11}-2\sin\frac{\pi}{22}-3}}$$ ≈ 1:1.37115.

Vertex coordinates
Coordinates for the vertices of an 11-3 step prism inscribed in a hendecagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 10. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to :$$\sqrt{\frac{1+2\sin\frac{3\pi}{22}}{2\cos\frac{\pi}{11}+2\sin\frac{\pi}{22}-1}}$$ ≈ 1:1.23333.
 * (a*sin(2πk/11), a*cos(2πk/11), b*sin(6πk/11), b*cos(6πk/11)),