10-2 step prism

The 10-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 5 rhombic disphenoids and 30 phyllic disphenoids of three kinds as cells, with 14 (2 rhombic and 12 phyllic disphenoids) joining at each vertex.

It is one of 4 isogonal polychora with 10 vertices, and the only one to have only step prism symmetry in its highest symmetry form.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{26+10\sqrt5}}{4}$$ ≈ 1:1.73855.

Vertex coordinates
Coordinates for the vertices of a 10-2 step prism inscribed in a decagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 9. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\frac{1+\sqrt5}{2}$$ ≈ 1:1.61803.
 * (a*sin(πk/5), a*cos(πk/5), b*sin(2πk/5), b*cos(2πk/5)),