18-3 step prism

The 18-3 step prism, also known as the 9-3 double step prism, is a convex isogonal polychoron and a member of the step prism family. It has 6 triangular gyroprisms and 72 phyllic disphenoids of four kinds as cells, with 16 phyllic disphenoids and 2 triangular gyroprisms joining at each vertex. It can also be constructed as the convex hull of two opposite 9-3 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{15+24\cos\frac{\pi}{9}}}{3}$$ ≈ 1:2.04267.

Vertex coordinates
Coordinates for the vertices of an 18-3 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:$$\sqrt{1+2\cos\frac\pi9}$$ ≈ 1:1.69688.
 * (a*sin(πk/9), a*cos(πk/9), b*sin(πk/3), b*cos(πk/3)),