11-2 step prism

The 11-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 44 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 11-5 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{12\sin\frac{\pi}{22}-4\cos\frac{\pi}{11}-5}{10\cos\frac{\pi}{11}+24\sin\frac{\pi}{22}-15}}$$ ≈ 1:1.89312.

Vertex coordinates
Coordinates for the vertices of an 11-2 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 :$$\frac{1}{\sqrt{2\cos\frac{\pi}{11}-2\cos\frac{2\pi}{11}}}$$ ≈ 1:2.05638.
 * (a*sin(2πk/11), a*cos(2πk/11), b*sin(4πk/11), b*cos(4πk/11)),