Great birhombatodecachoron

The great birhombatodecachoron or gabred is a convex isogonal polychoron that consists of 10 rhombitetratetrahedra, 20 triangular antiprisms, 60 rectangular pyramids, and 30 tetragonal disphenoids 2 rhombitetratetrahedra, 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. In this case, the ratio between the edges of the small rhombated pentachoron a3o3b3o is greater than b:a = 3 (which produces the rectified decachoron in the limiting case). The lacing edges generally have length $$\sqrt{\frac{3a^2-2ab+2b^2}{5}}$$.