Small transitional 13-5 double step prism

The small transitional 13-5 double step prism is a convex isogonal polychoron that consists of 26 bilaterally-symmetric octahedra and 13 tetragonal disphenoids. 6 bilaterally-symmetric octahedra and 2 tetragonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal 13-5 step prisms.

The ratio between the longest and shortest edges is 1:a ≈ 1:2.15664, where a is the largest real root of a6-7a4+12a2-5.

Vertex coordinates
Coordinates for the vertices of a small transitional 13-5 double step prism are given by: where a = 1/($\sqrt{2}$(sin(5π/26)csc(π/26)-1)), b = sin(5π/26)/($\sqrt{2}$(sin(5π/26)-sin(π/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)),