In recent years, BN fullerenes have been synthesized experimentally. As their carbon counterparts, these BN fullerenes could be assembled in molecular solids, but this possibility has been studied little in the literature. In this work, we focus on the smallest synthesized BN fullerene, B12N12, which is built by squares and hexagons. First, the interaction between two of these fullerenes has been analyzed, using the hybrid B3LYP and MPW1PW91 density functional methods. Two different interactions have been studied in the dimer, a square facing a square (S−S) and a hexagon facing a hexagon (H−H). In both cases, a B is facing a N. The most stable dimer was found to be S−S facing, with covalent interactions between the monomers, but other dimers with weak interactions have been found as well, which opens possibilities of new systems, as in the case of fullerene dimers and solids. The solids resulting from the infinite repetition of the characterized dimers were optimized, finding two different solids, with co...