18-6 step prism

The 18-6 step prism is a convex isogonal polychoron and a member of the step prism family. It has 3 hexagonal gyroprisms and 18 phyllic disphenoids as cells, with 4 phyllic disphenoids and 2 hexagonal gyroprisms joining at each vertex.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{1+2\cos\frac{\pi}{9}-2\cos\frac{2\pi}{9}}$$ ≈ 1:1.16073.

Vertex coordinates
Coordinates for the vertices of an 18-6 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:$$\sqrt{\frac{2\cos\frac\pi9-1}{3}}$$ ≈ 1:0.54141.
 * (a*sin(πk/9), a*cos(πk/9), b*sin(2πk/3), b*cos(2πk/3)),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Phyllic disphenoid (18): 18-6 step prism
 * Scalene triangle (18): 18-6 step prism
 * Scalene triangle (36): 36-6 step prism
 * Edge (18): 18-6 step prism