The production of boron nitride nanotubes has prompted numerous investigations into the structural properties of intermediate-sized boron nitride molecules. For molecules with more than twenty atoms, cage isomers are the most stable. In this study, two classes of boron nitrides are compared: fullerene-like structures consisting of pentagons and hexagons, and alternant structures consisting of squares and hexagons. These two classes are compared for B 1 3 N 1 3 , B 1 4 N 1 4 , and B 1 6 N 1 6 by theoretical calculations using Hartree-Fock theory and density functional theory (B3LYP and LDA). The major result is that the alternant structures are more stable than the molecules based on fullerenes.