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. Together with its dual, it is the second in an infinite family of triangular dihedral swirlchora.

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

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:$$\frac{1}{\sqrt{2\cos\frac\pi9-2\sin\frac{\pi}{18}}}$$ ≈ 1:0.80790.
 * (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