20-3 step prism

The 20-3 step prism is a convex isogonal polychoron and a member of the step prism family. It has 120 phyllic disphenoids of six kinds as cells, with 24 joining at each vertex. It can also be constructed as the 20-7 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{16}{8-\sqrt{50-10\sqrt5}}-1}$$ ≈ 1:2.19857.

Vertex coordinates
Coordinates for the vertices of a 20-3 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:$$\sqrt{2+\sqrt5}$$ ≈ 1:2.05817.
 * (a*sin(πk/10), a*cos(πk/10), b*sin(3πk/10), b*cos(3πk/10)),