20-5 step prism

The 20-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 4 pentagonal gyroprisms and 40 phyllic disphenoids of two kinds as cells, with 8 phyllic disphenoids and 2 pentagonal gyroprisms joining at each vertex.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{50-50\sqrt5+40\sqrt{25+10\sqrt5}}}{10}$$ ≈ 1:1.46107.

Vertex coordinates
Coordinates for the vertices of a 20-5 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:$$\frac{\sqrt{1-\sqrt5+\sqrt{10+2\sqrt5}}}{2}$$ ≈ 1:0.80127.
 * (a*sin(πk/10), a*cos(πk/10), b*sin(πk/2), b*cos(πk/2)),