26-5 step prism

The 26-5 step prism is a convex isogonal polychoron, member of the step prism family. It has 26 tetragonal disphenoids and 156 phyllic disphenoids of three kinds as cells. 4 tetragonal and 24 phyllic disphenoids join at each vertex.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2+\cos\frac{2\pi}{13}-\cos\frac{3\pi}{13}}{2-\cos\frac{\pi}{13}-\sin\frac{3\pi}{26}}}$$ ≈ 1:1.78000.

Vertex coordinates
Coordinates for the vertices of a 26-5 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 25.
 * (sin(πk/13), cos(πk/13), sin(5πk/13), cos(5πk/13)),