Tridecagonal duotegum

The great 13-5 double step prism is a convex isogonal polychoron that consists of 13 rhombic disphenoids, 156 irregular tetrahedron|irregular tetrahedra]] of three kinds obtained as the convex hull of two orthogonal 13-5 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution (a/b = (2+$\sqrt{4+2cos(π/13)+2sin(3π/26)}$)/(2cos(2π/13)) would yield a small 13-5 double step prism instead.

Vertex coordinates
Coordinates for the vertices of a great 13-5 double step prism are given by: where a/b is less than 0.06639210591383135938730809 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)),