Great transitional 12-5 double step prism

The great transitional 12-5 double step prism is a convex isogonal polychoron that consists of 12 digonal scalenohedra, 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.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{30}}{2}$$ ≈ 1:2.73861.

Vertex coordinates
Coordinates for the vertices of a great transitional 12-5 double step prism are given by: where a = (2-$\sqrt{3}$)/2, b = (2+$\sqrt{3}$)/2 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)),