10-2 double step prism

The 10-2 double step prism is a convex isogonal polychoron that consists of 20 tetragonal disphenoids, 20 rhombic disphenoids, and 40 phyllic disphenoids. 4 tetragonal disphenoids, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as the convex hull of two opposite 10-2 step prisms.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{176+44\sqrt5}}{11}$$ ≈ 1:1.50588.

Vertex coordinates
Coordinates for the vertices of a 10-2 double step prism are given by: where a = 1/2 and k is an integer from 0 to 9.
 * (a*sin(2πk/10), a*cos(2πk/10), a*sin(6πk/10), a*cos(6πk/10)),
 * (a*sin(2πk/10), a*cos(2πk/10), -a*sin(6πk/10), -a*cos(6πk/10)),