- Heteroatomic cages (BN/2NN/2) with borons and nitrogens fully replacing alternant sets of carbons in cages are built graph-theoretically and investigated via the semiempirical MNDO Hamiltonian. The comparison with their parent carbon cages CN is made in terms both of electronic and of geometric changes. Infinite classes first of octahedral symmetry and second of hexagonal-bipyramidal symmetry fullerenoid cages are considered in detail The difference in the electronegativities for boron and nitrogen implies the opening of HOMO-LUMO gaps for alternant BN clusters. In general, the borons prefer planar geometry (sp2 hybridization) while the nitrogens prefer pyramidalization (sp3 hybridization). © 1997 John Wiley & Sons. Inc.