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 gyroprisms and 15 phyllic disphenoids as cells, with 4 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:$$\frac{\sqrt{5+\sqrt5-\sqrt{6-\frac{6}{\sqrt5}}}}{2}$$ ≈ 1:1.16349.

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