Molecular complexes of a fullerene analogue B12N12 with hydrogen halides (HCl, HBr, and HI) were Studied with symmetry-adapted perturbation theory with density-functional theory applied for a description of monomers (SAPT(DFT)), Moller-Plesset theory to the second order (MP2), and its spin-component-scaled variant (SCS-MP2) in a limit of a complete basis set. For each halide five syrnmetry-distinct minimum structures of the complex have been found on the potential energy hypersurface, with interaction energies ranging from -6 to -18 kJ/mol. The natural bond orbital and the atom-in-Molecules analysis of noncovalent bonds resulted in a division of these configurations into three categories: hydrogen bonded, halogen bonded, and those of a mixed type, involving simultaneously a hydrogen bonding and a pi-hole bonding between halogen and boron atoms. A comparison of various approaches for the calculation of interaction energies shows that the SCS-MP2 supermolecular method gives results Which are in a doe agreement with SAPT(DFT), while the MP2 interaction energies are systematically more negative than the SAPT values. The ability of the B12N12 nanocage to bind hydrogen halides through several active sites on its surface puts under question the selectivity of the binding necessary in crystal engineering, especially for the hydrogen bromide and hydrogen iodide cases, which show small differences in stabilization energies for their minimum structures. The directionality of noncovalent bonds is explained on grounds of the anisotropy of some SAPT components, like electrostatics and induction, as well as by the sigma-hole and pi-hole models.