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 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:$$\frac{\sqrt{7+\sqrt21}}{2}$$ ≈ 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)),