Small 13-5 double step prism

The 13-5 double step prism is a convex isogonal polychoron that consists of 13 rhombic disphenoids, 26 phyllic disphenoids of two kinds and 52 irregular tetrahedra obtained as the convex hull of two orthogonal 13-5 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:1.58440.

Vertex coordinates
Coordinates for the vertices of a small 13-5 double step prism are given by: where a = $\sqrt{2}$/(2sec(2π/13)+sec(2π/13)$\sqrt{4+2cos(π/13)+2sin(3π/26)}$-2), b = ($\sqrt{2}$+$\sqrt{2+cos(π/13)+sin(3π/26)}$)/(2-2cos(2π/13)+$\sqrt{4+2cos(π/13)+2sin(3π/26)}$) and k is an integer from 0 to 12.
 * (a*sin(2πk/13), a*cos(2πk/13), b*sin(10πk/13), b*cos(10πk/13)),
 * (b*sin(2πk/13), b*cos(2πk/13), a*sin(10πk/13), a*cos(10πk/13)),