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 mirror-symmetric hexatera and 18 irregular hexatera as peta.

It is the simplest step prism, excluding the heptapeton and the tetrahedral duotegum, which are part of more specific families, as well as the one of two isogonal polychora 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)),