19-7 step prism

The 19-7 step prism is a convex isogonal polychoron and a member of the step prism family. It has 76 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 19-8 step prism. It is also the heptagonal funk tegum.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately 1:1.67674.

Vertex coordinates
Coordinates for the vertices of a 19-7 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:$$\sqrt{\frac{\cos\frac{2\pi}{19}+\cos\frac{3\pi}{19}}{\cos\frac{2\pi}{19}+\cos\frac{5\pi}{19}}}$$ ≈ 1:1.06046.
 * (a*sin(2πk/19), a*cos(2πk/19), b*sin(14πk/19), b*cos(14πk/19)),