15-4 step prism

The 15-4 step prism is a convex isogonal polychoron and a member of the step prism family. It has 60 phyllic disphenoids of two kinds as cells, with 16 joining at each vertex. Together with its dual, it is the fourth in an infinite family of triangular dihedral swirlchora.

Compared to other 15-vertex step prisms, this polychoron has doubled symmetry, because 15 = 42-1.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{594+154\sqrt5}}{22}$$ ≈ 1:1.39239.

Vertex coordinates
Coordinates for the vertices of a 15-4 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 14.
 * (sin(2πk/15), cos(2πk/15), sin(8πk/15), cos(8πk/15)),