14-3 step prism

The 14-3 step prism, also known as the 7-2 double step prism, is a convex isogonal polychoron and a member of the step prism family. It has 56 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 14-5 step prism, or as the convex hull of two opposite 7-2 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{1-\sin\frac{\pi}{14}+2\cos\frac{\pi}{7}}{\sin\frac{\pi}{14}+2\cos\frac{\pi}{7}-1}}$$ ≈ 1:1.58677.

Vertex coordinates
Coordinates for the vertices of a 14-3 step prism inscribed in a tetradecagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 13. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\sqrt{\frac{2\cos\frac\pi7+2\sin\frac{\pi}{14}-1}{1-2\sin\frac{\pi}{14}}}$$ ≈ 1:1.49899.
 * (a*sin(πk/7), a*cos(πk/7), b*sin(3πk/7), b*cos(3πk/7)),