17-5 step prism

The 17-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 68 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 17-7 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately 1:1.55810.

Vertex coordinates
Coordinates for the vertices of a 17-5 step prism inscribed in a heptadecagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 16. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\sqrt{\frac{\cos\frac{3\pi}{17}+\cos\frac{4\pi}{17}}{\cos\frac{2\pi}{17}+\cos\frac{3\pi}{17}}}$$ ≈ 1:0.94418.
 * (a*sin(2πk/17), a*cos(2πk/17), b*sin(10πk/17), b*cos(10πk/17)),