Transitional 12-5 double gyrostep prism

The transitional 12-5 double gyrostep prism is a convex isogonal polychoron that consists of 24 tetragonal antiwedges, 24 tetragonal disphenoids, and 24 phyllic disphenoids. 6 tetragonal antiwedges, 4 tetragonal disphenoids, and 4 phyllic 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:$$\sqrt{4+2\sqrt2}$$ ≈ 1:2.61313.

Vertex coordinates
Coordinates for the vertices of a transitional 12-5 double gyrostep 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)),