42-13 step prism

The 42-13 step prism is a convex isogonal polychoron, member of the step prism family. It has 42 rhombic disphenoids and 252 phyllic disphenoids of three kinds as cells. 4 rhombic and 24 phyllic disphenoids join at each vertex. It is also the 42-29 step prism.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{7+46\cos\frac{2\pi}{7}}{16\cos\frac{2\pi}{7}-6}}$$ ≈ 1:2.99572.

Vertex coordinates
Coordinates for the vertices of a 42-13 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 40.
 * (sin(πk/21), cos(πk/21), sin(13πk/21), cos(13πk/21)),