16-4 step prism

The 16-4 step prism is a convex isogonal polychoron and a member of the step prism family. It has 4 square gyroprisms and 32 phyllic disphenoids of two kinds as cells, with 8 phyllic disphenoids and 2 square gyroprisms joining at each vertex.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{4-2\sqrt2+4\sqrt{2+\sqrt2}}}{2}$$ ≈ 1:1.46310.

Vertex coordinates
Coordinates for the vertices of a 16-4 step prism inscribed in a hexadecagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 15. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\frac{\sqrt[4]{8+4\sqrt2}}{2}$$ ≈ 1:0.96119.
 * (a*sin(πk/8), a*cos(πk/8), b*sin(πk/2), b*cos(πk/2)),