Great 12-5 double step prism

The great 12-5 double step prism is a convex isogonal polychoron that consists of 12 tetragonal disphenoids, 24 rhombic disphenoids of two kinds, 24 phyllic disphenoids and 96 irregular tetrahedra of two kinds 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 = $\sqrt{33+12√7}$/3) would yield a small 12-5 double step prism instead.

Vertex coordinates
Coordinates for the vertices of a great 12-5 double step prism are given by: where a/b is greater than 7-4$\sqrt{3}$ but less than 2-$\sqrt{3}$ 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)),