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.

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 7. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\sqrt{\frac{5+\sqrt5}{8}}$$ ≈ 1:0.85065.
 * (a*sin(πk/5), a*cos(πk/5), b*sin(2πk/5), b*cos(2πk/5)),