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 obtained as the convex hull of two orthogonal 12-5 step prisms.

The ratio between the longest and shortest edges is 1:$\sqrt{3}$ ≈ 1:1.73205.

Vertex coordinates
Coordinates for the vertices of a small transitional 12-5 double step prism are given by: where a = $\sqrt{36-6√18-12√2}$/12, b = $\sqrt{36+6√18-12√2}$/12 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)),