19-3 step prism

The 19-3 step prism is a convex isogonal polychoron and a member of the step prism family. It has 114 phyllic disphenoids of six kinds as cells, with 24 joining at each vertex. It can also be constructed as the 19-6 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately 1:2.12612.

Vertex coordinates
Coordinates for the vertices of a 19-3 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:$$\sqrt{\frac{\cos\frac{7\pi}{19}+\cos\frac{2\pi}{19}}{\cos\frac{2\pi}{19}-\cos\frac{6\pi}{19}}}$$ ≈ 1:1.83802.
 * (a*sin(2πk/19), a*cos(2πk/19), b*sin(6πk/19), b*cos(6πk/19)),