In the polyhedral BNHN series, charge states are -2 for N = 12 (the known B12H12-2 ion), Zero for N = 16 (T-d symmetry), -2 for N = 32 (I-h symmetry, the dual polyhedron of the C-60 fullerene), -2 for N = 37 (D-5h symmetry) and -2 for N = 42 (I-h symmetry), as calculated by ab initio (3-21G level), PRDDO (partial retention of diatomic differential overlap), AM1 (semiempirical), and LDF (local density functional) methods. These methods are in agreement, although the AM1 results did nor converge for N = 37. The most stable species per BH unit is B12H122-, and the next most stable is predicted to be B42H422-.