Small birhombatodecachoron

The small birhombatodecachoron or sabred is a convex isogonal polychoron that consists of 10 octahedra, 20 triangular antiprisms, 40 triangular antipodiums, and 30 tetragonal disphenoids. 1 octahedron, 2 triangular antiprisms, 4 triangular antipodiums, and 2 tetragonal disphenoids join at each vertex.

It is one of a total of five distinct polychora (including 3 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 between b:a = 1/2 (producing the rectified small prismatodecachoron) and b:a = 3 (producing the recitifed decachoron).