16-3 step prism

The 16-3 step prism is a convex isogonal polychoron and a member of the step prism family. It has 80 phyllic disphenoids of five kinds as cells, with 20 joining at each vertex. It can also be constructed as the 16-5 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{2\sqrt2+2\sqrt{2-sqrt2}-1}$$ ≈ 1:1.83280.

Vertex coordinates
Coordinates for the vertices of a 16-3 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:$$\sqrt{1+\sqrt2}$$ ≈ 1:1.55377.
 * (a*sin(πk/8), a*cos(πk/8), b*sin(3πk/8), b*cos(3πk/8)),