A systematic theoretical analysis of homopolar dihydrogen interactions in group 13 compounds is presented here. Ab initio calculations and structural analysis allow us to demonstrate that interactions involving B–H⋯H–B contacts are comparable in strength to the previously studied C–H⋯H–C ones, yet attractive and important for the stabilization of dimers of large molecules. We have also shown that a polyhedral skeleton enhances the B–H⋯H–B interaction strength with respect to non-polyhedral compounds, and it has also been proven that Al–H⋯H–Al and Ga–H⋯H–Ga interactions can be attractive in some cases. If H⋯E (B, Al and Ga) short contacts are present, the interaction is significantly strengthened, especially for Al and Ga. In general, H⋯H interactions combined with associated H⋯E (B, Al and Ga) short contacts are responsible for the stability of a large number of dimers of group 13 compounds and may play an important role in the packing of their crystal structures.