12-5 double gyrostep prism

The 12-5 double gyrostep prism is a convex isogonal polychoron that consists of 12 tetragonal disphenoids, 24 rhombic disphenoids of two kinds, 24 phyllic disphenoids and 48 irregular tetrahedra. 12 phyllic disphenoids and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution (a/b = $$1+\sqrt2$$) would yield a 24-5 step prism instead.

Vertex coordinates
Coordinates for the vertices of a 12-5 double gyrostep prism are given by: where a/b is greater than $\sqrt{2-√3}$ but less than 2$\sqrt{3}$+$\sqrt{14-8√3}$-3 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)),