17-4 step prism

The 17-4 step prism is a convex isogonal polychoron, member of the step prism family. It has 17 tetragonal disphenoids and 68 phyllic disphenoids of two kinds as cells. 2 tetragonal and 16 phyllic disphenoids join at each vertex.

Compared to other 17-vertex step prisms, this polychoron has doubled symmetry, because 17 = 42+1.

The ratio between the longest and shortest edges is 1:\frac{\sqrt{871+13\sqrt{17}+13\sqrt{1802+134\sqrt{17}}}{26} ≈ 1:1.51687.

Vertex coordinates
Coordinates for the vertices of a 17-4 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 16.
 * (sin(2πk/17), cos(2πk/17), sin(8πk/17), cos(8πk/17)),