18-5 step prism

The 18-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 72 phyllic disphenoids of four kinds as cells, with 16 joining at each vertex. It can also be constructed as the 18-7 step prism. . Together with its dual, it is the fifth in an infinite family of triangular dihedral swirlchora and the second in an infinite series of hexagonal dihedral swirlchora.

Vertex coordinates
Coordinates for the vertices of an 18-5 step prism inscribed in an octadecagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 17. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\sqrt{\frac{\cos\frac{2\pi}{9}}{\cos\frac\pi9}}$$ ≈ 1:0.90289.
 * (a*sin(πk/9), a*cos(πk/9), b*sin(5πk/9), b*cos(5πk/9)),