20-4 step prism

The 20-4 step prism is an isogonal polychoron and a member of the step prism family. It has 5 square gyroprisms and 60 phyllic disphenoids of three kinds as cells, with 12 phyllic disphenoids and 2 square gyroprisms joining at each vertex.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:\frac{\sqrt{4+2\sqrt{10+2\sqrt5}}}{2} ≈ 1:1.70356.

Vertex coordinates
Coordinates for the vertices of a 20-4 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:$$\frac{\sqrt[4]{625+250\sqrt5}}{5}$$ ≈ 1:1.17319.
 * (a*sin(πk/10), a*cos(πk/10), b*sin(2πk/5), b*cos(2πk/5)),