ne structural principles of perhydrogenated boron nitride fullerenes have been determined by quantum chemical calculations. The octahedral boron nitride fullerenes were classified into structural families, which were I systematically studied. Each family was developed into a series of cages, up to B444N444H888, subjecting them to perhydrogenation. Chiral, T-symmetric nanostructures are favored in energy, possessing an optimal diameter of around 2.8 nm, corresponding to a molecular formula of B228N228H456. The facets of the octahedral nanostructures are clearly curved, placing B-H bonds on the convex side and N-H bonds on the concave side. The curvature is due to the partially ionic character of the B-N bond, which polarizes the hydrogen atoms. The described structural principles of perhydrogenated boron nitride fullerenes are expected to provide new insight into structural characteristics and properties of novel nanomaterials based on group 13-15 binary compounds.