Medial birhombatodecachoron

The medial birhombatodecachoron or mabred is a convex isogonal polychoron that consists of 10 octahedra, 20 triangular prisms, 20 triangular antiprisms, 60 rectangular pyramids, and 30 tetragonal disphenoids. 1 octahedron, 2 triangular prisms, 2 triangular antiprisms, 5 rectangular pyramids, and 2 tetragonal disphenoids join at each vertex.

It is one of a total of five distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite small rhombated pentachora, where the ratio between the edges of the small rhombated pentachoron a3o3b3o is less than b:a = 1/2 (which produces the rectified small prismatodecachoron in the limiting case). The lacing edges generally have length $$\sqrt{\frac{3a^2-2ab+2b^2}{5}}$$.