19-2 step prism

The 19-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 152 phyllic disphenoids of eight kinds as cells, with 32 joining at each vertex. It can also be constructed as the 19-9 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately 1:3.10417.

Vertex coordinates
Coordinates for the vertices of a 19-2 step prism inscribed in an enneadecagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 18. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\frac{1}{\sqrt{2\cos\frac{\pi}{19}-2\cos\frac{2\pi}{19}}}$$ ≈ 1:3.51173.
 * (a*sin(2πk/19), a*cos(2πk/19), b*sin(4πk/19), b*cos(4πk/19)),