Small birhombatotetracontoctachoron

The small birhombatotetracontoctachoron or sabric is a convex isogonal polychoron that consists of 48 cuboctahedra, 144 square antiprisms, 384 triangular antipodiums, and 288 tetragonal disphenoids. 1 cuboctahedron, 2 square antiprisms, 4 triangular antipodiums, 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 icositetrachora. In this case, the ratio between the edges of the small rhombated icositetrachoron a3o4b3o is between b:a = 1/2 (producing the rectified small prismatotetracontoctachoron) and b:a = 2+$\sqrt{2}$ (producing the rectified tetracontoctachoron). This includes the convex hull of two uniform small rhombated icositetrachora. The lacing edges generally have length $$\sqrt{(2-\sqrt2)a^2-(6-4\sqrt2)ab+(6-4\sqrt2)b^2}$$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2+\sqrt2}{2}}$$ ≈ 1:1.30656.