9-2-3 step prism

The 9-2-3 step prism is a convex isogonal polypeton and a member of the step prism family. It has 3 triangular disphenoids, 9 bilaterally-symmetric hexatera and 18 irregular hexatera as peta. 2 disphenoids, along with 6 bilaterally-symmetric and 12 irregular hexatera, join at each vertex.

It is the simplest 6D step prism, excluding the 7-2-3 step prism (better known as the heptapeton) and the 8-2-3 step prism (better known as the tetrahedral duotegum), as well as the one of two isogonal polypeta with 9 vertices, the other being the triangular triotegum.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{2\cos\frac{2\pi}{9}}$$ ≈ 1:1.23778.

Vertex coordinates
Coordinates for the vertices of a 9-2-3 step prism inscribed in an enneagonal trioprism with base lengths a, b and c 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:c must be equivalent to 1:$$\frac{1}{\sqrt{2\cos\frac{2\pi}{9}}}$$:$$\sqrt{\frac{2\cos\frac\pi{18}}{\sqrt3}}$$ ≈ 1:0.80790:1.06638.
 * (a*sin(2πk/9), a*cos(2πk/9), b*sin(4πk/9), b*cos(4πk/9), c*sin(6πk/9), c*cos(6πk/9)),