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 four kinds as cells. It is also the 45-26 step prism.

The ratio between the longest and shortest edges is 1:$\sqrt{2-cos(2π/45)+cos(7π/45)}$/(2sin(π/9)) ≈ 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)),