9-2 step prism

The 9-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 27 phyllic disphenoids of three kinds as cells, with 12 joining at each vertex. It can also be constructed as the 9-4 step prism.

It is one of 3 isogonal polychora with 9 vertices, the others are the uniform triangular duoprism and the 9-3 step prism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2\cos\frac{\pi}{9}}{\cos\frac{2\pi}{9}}}$$ ≈ 1:1.56632.

Vertex coordinates
Coordinates for the vertices of a 9-2 step prism inscribed in an enneagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 8. 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(2πk/9), a*cos(2πk/9), b*sin(4πk/9), b*cos(4πk/9)),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Phyllic disphenoid (9): 9-2 step prism
 * Scalene triangle (9): 9-2 step prism
 * Scalene triangle (19): 18-2 step prism
 * Edge (9): 9-2 step prism