15-6 step prism

The 15-6 step prism is a convex isogonal polychoron and a member of the step prism family. It has 5 triangular gyroprisms and 30 phyllic disphenoids of two kinds as cells, with 8 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:$$\sqrt{\frac{3}{3-\sqrt{15-6\sqrt5}}}$$ ≈ 1:1.31246.

Vertex coordinates
Coordinates for the vertices of a 15-6 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:$$\frac{\sqrt{50+10\sqrt{75-30\sqrt5}}}{10}$$ ≈ 1:0.88396.
 * (a*sin(2πk/15), a*cos(2πk/15), b*sin(4πk/5), b*cos(4πk/5)),