20-8 step prism

The 20-8 step prism is a convex isogonal polychoron and a member of the step prism family. It has 5 square gyroprisms and 40 phyllic disphenoids of two kinds as cells, with 8 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:$$\sqrt{\sqrt{10+2\sqrt5}-2}$$ ≈ 1:1.34321.

Vertex coordinates
Coordinates for the vertices of a 20-8 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:$$\frac{\sqrt[4]{5000-1000\sqrt5}}{10}$$ ≈ 1:0.72507.
 * (a*sin(πk/10), a*cos(πk/10), b*sin(4πk/5), b*cos(4πk/5)),