9-2 step prism

The 9-2 step prism is a convex isogonal polychoron, member of the step prism family. It has 27 phyllic disphenoids of three kinds as cells, with 12 joining at each vertex. 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 heptagonal 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 :$$\frac{1}{\sqrt{2\cos\frac\pi9-2\sin\frac{\pi}{18}}$$ ≈ 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