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 is also the heptagonal funk tegum.

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:$$\sqrt{\frac{\cos\frac{2\pi}{19}+\cos\frac{3\pi}{19}}{\cos\frac{2\pi}{19}+\cos\frac{5\pi}{19}}}$$ ≈ 1:1.06046.
 * (a*sin(2πk/19), a*cos(2πk/19), b*sin(14πk/19), b*cos(14πk/19)),