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, and 72 phyllic disphenoids of two kinds. 3 digonal scalenohedra, 4 rhombic disphenoids, and 12 phyllic disphenoids join at each vertex. It can be 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)),