9-3 step prism

The 9-3 step prism is a convex isogonal polychoron and a member of the step prism family. It has 3 chiral triangular antiprisms and 9 phyllic disphenoids as cells, with 4 disphenoids and 2 antiprisms joining at each vertex..

It is one of three isogonal polychora with 9 vertices (the others are the 9-2 step prism and triangular duoprism), as well as the simplest step prism to have cells other than tetrahedra.

Vertex coordinates
Coordinates for the vertices of a 9-3 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:$$\sqrt{\frac{1+2\cos\frac{2\pi}{9}}{3}}$$ ≈ 1:0.91871.
 * (a*sin(2πk/9), a*cos(2πk/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 (9): 9-3 step prism
 * Scalene triangle (9): 9-3 step prism
 * Scalene triangle (18): 18-3 step prism
 * Edge (9): 9-3 step prism