39-14 step prism

The 39-14 step prism is a convex isogonal polychoron, member of the step prism family. It has 234 phyllic disphenoids of three kinds as cells. 24 disphenoids join at each vertex. It is also the 39-25 step prism.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{2-\cos\frac{2\pi}{39}+\sin\frac{17\pi}{78}}}{2\sin\frac{\pi}{13}}$$ ≈ 1:2.67999.

Vertex coordinates
Coordinates for the vertices of a 39-14 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 38.
 * (sin(2πk/39), cos(2πk/39), sin(28πk/39), cos(28πk/39)),