Small 12-5 double step prism

The small 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 48 irregular tetrahedra. 2 tetragonal disphenoid, 4 rhombic disphenoids, 4 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{7+\sqrt{21}}}{2}$$ ≈ 1:1.70166.

Vertex coordinates
Coordinates for the vertices of a small 12-5 double step prism are given by: where a = $\sqrt{7-2√7+√33-12√7}$/4, b = $\sqrt{7+2√7+√33+12√7}$/4 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)),