15-5 step prism

The 15-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 3 pentagonal antiprisms and 15 phyllic disphenoids as cells, with 4 disphenoids and 2 antiprisms joining at each vertex.

Vertex coordinates
Coordinates for the vertices of a 15-5 step prism inscribed in a pentadecagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 14. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\sqrt{\frac{3-\sqrt5+\sqrt{30-6\sqrt5}}{12}}$$ ≈ 1:0.63484.
 * (a*sin(2πk/15), a*cos(2πk/15), b*sin(2πk/3), b*cos(2πk/3)),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Phyllic disphenoid (15): 15-5 step prism
 * Scalene triangle (15): 15-5 step prism
 * Scalene triangle (30): 30-5 step prism
 * Edge (15): 15-5 step prism