45-19 step prism

The 45-19 step prism is a convex isogonal polychoron, member of the step prism family. It has 270 phyllic disphenoids of three kinds as cells. 24 disphenoids join at each vertex. It is also the 45-26 step prism.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{2-\cos\frac{2\pi}{45}+\cos\frac{7\pi}{45}}}{2\sin\frac\pi9}$$ ≈ 1:2.01121.

Vertex coordinates
Coordinates for the vertices of a 45-19 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 44.
 * (sin(2πk/45), cos(2πk/45), sin(38πk/45), cos(38πk/45)),