Medial 13-5 double step prism

The medial 13-5 double step prism is a convex isogonal polychoron that consists of 13 tetragonal disphenoids, 26 phyllic disphenoids and 104 irregular tetrahedra of two 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.