15-3 step prism

The 15-3 step prism is an isogonal polychoron and a member of the step prism family. It has 5 triangular gyroprisms and 45 phyllic disphenoids of three kinds as cells, with 12 phyllic disphenoids and 2 triangular gyroprisms joining at each vertex.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{60+6\sqrt5+6\sqrt{15+6\sqrt5}}}{6}$$ ≈ 1:1.71108.

Vertex coordinates
Coordinates for the vertices of a 15-3 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:$$\frac{\sqrt{75+25\sqrt5+5\sqrt{150+30\sqrt5}}}{10}$$ ≈ 1:1.43028.
 * (a*sin(2πk/15), a*cos(2πk/15), b*sin(2πk/5), b*cos(2πk/5)),