12-5 double gyrostep prism

The small 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 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+$\sqrt{2}$) would yield a dodecagonal duotegum variant instead.

Vertex coordinates
Coordinates for the vertices of a small 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)),