19-4 step prism

The 19-4 step prism is a convex isogonal polychoron and a member of the step prism family. It has 95 phyllic disphenoids of five kinds as cells, with 20 joining at each vertex. It can also be constructed as the 19-5 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately 1:1.59884.

Vertex coordinates
Coordinates for the vertices of a 19-4 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:$$\sqrt{\frac{\cos\frac{2\pi}{19}+\sin\frac{\pi}{38}}{\cos\frac{2\pi}{19}-\sin\frac{3\pi}{38}}}$$ ≈ 1:1.21179.
 * (a*sin(2πk/19), a*cos(2πk/19), b*sin(8πk/19), b*cos(8πk/19)),