Small 12-5 double step prism

The small 12-5 double step prism is a convex isogonal polychoron that consists of 12 tetragonal disphenoids, 48 phyllic disphenoids of two kinds 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:$\sqrt{7+√21}$/2 ≈ 1:1.70166.

Vertex coordinates
Coordinates for the vertices of a small 10-3 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 12.
 * (a*sin(2πk/10), a*cos(2πk/10), b*sin(6πk/10), b*cos(6πk/10)),
 * (b*sin(2πk/10), b*cos(2πk/10), a*sin(6πk/10), a*cos(6πk/10)),