20-2 step prism

The 20-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 10 rhombic disphenoids and 160 phyllic disphenoids of eight kinds as cells, with 34 (2 rhombic and 32 phyllic disphenoids) joining at each vertex.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:\frac{\sqrt{14+4\sqrt5+2\sqrt{50+22\sqrt5}}}{2} ≈ 1:3.27351.

Vertex coordinates
Coordinates for the vertices of a 20-2 step prism inscribed in an icosagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 19. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\frac{\sqrt{12+4\sqrt5+2\sqrt{50+22\sqrt5}}}{2}$$ ≈ 1:3.19623.
 * (a*sin(πk/10), a*cos(πk/10), b*sin(πk/5), b*cos(πk/5)),