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. 2 tetragonal disphenoids, 4 rhombic disphenoids, 4 phyllic disphenoids, and 16 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 = $\sqrt{33+12√7}$/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)),