18-5 step prism

The 18-5 step prism, also known as the 9-2 double 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, or as the convex hull of two opposite 9-2 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt2$$ ≈ 1:1.41421.

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)),