The atomic structure, stability, and electronic structure of, and interatomic interaction in the Be4O4, Be12O12 and Be16O16 natioclusters are investigated by self-consistent ab initio Hartree-Fock and density functional theory calculations using the discrete variational method. These properties are analyzed as a function of cluster geometry and are discussed with reference to the electronic properties of wurtzite-like BeO. Among the beryllium oxide clusters, the polyhedral (fullerene-like) clusters are stable. Luminescent and exoemission properties are anticipated for some nanoclusters.