29-12 step prism

The 29-12 step prism is a convex isogonal polychoron, member of the step prism family. It has 29 tetragonal disphenoids and 116 phyllic disphenoids of two kinds as cells, with 20 (4 tetragonal and 16 phyllic disphenoids) joining at each vertex.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2-\cos\frac{2\pi}{29}+\cos\frac{5\pi}{29}}{2-\sin\frac{9\pi}{58}-\cos\frac{4\pi}{29}}}$$ ≈ 1:1.73583.

Compared to other 29-vertex step prisms, this polychoron has doubled symmetry, because 29 is a factor of 122+1 = 145.

Vertex coordinates
Coordinates for the vertices of a 29-12 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 28.
 * (sin(2πk/29), cos(2πk/29), sin(24πk/29), cos(24πk/29)),