Small transitional 12-5 double step prism

The small transitional 12-5 double step prism is a convex isogonal polychoron that consists of 12 rectangular antiprisms and 12 tetragonal disphenoids. 2 rectangular antiprisms and 4 tetragonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.

The ratio between the longest and shortest edges is 1:$$\sqrt3$$ ≈ 1:1.73205.

Vertex coordinates
Coordinates for the vertices of a small transitional 12-5 double step prism are given by: where a = ($\sqrt{3}$-1)/4, b = (1+$\sqrt{3}$)/4 and k is an integer from 0 to 11.
 * (a*sin(2πk/12), a*cos(2πk/12), b*sin(10πk/12), b*cos(10πk/12)),
 * (b*sin(2πk/12), b*cos(2πk/12), a*sin(10πk/12), a*cos(10πk/12)),