13-5 step prism

The 13-5 step prism is a convex isogonal polychoron and a member of the step prism family. It has 13 tetragonal disphenoids and 26 phyllic disphenoids as cells. 4 tetragonal and 8 phyllic disphenoids join at each vertex. It is also the pentagonal funk tegum.

Compared to other 13-vertex step prisms, this polychoron has doubled symmetry, because 13 is a factor of 52+1 = 26.

Its vertex figure is topologically equivalent to the Johnson solid snub disphenoid.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2-\cos\frac{2\pi}{13}+\cos\frac{3\pi}{13}}{2-\sin\frac{\pi}{26}-\sin\frac{5\pi}{26}}}$$ ≈ 1:1.19192.

Vertex coordinates
Coordinates for the vertices of a 13-5 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 12.
 * (sin(2πk/13), cos(2πk/13), sin(10πk/13), cos(10πk/13)),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Tetragonal disphenoid (13): 13-5 step prism
 * Edge (26): 13-5 double step prism
 * Edge (26): Small 13-5 double gyrostep prism