In this work we calculated the electronic structure of spherical quantum dots based on zincblend semiconductor compounds. The strong conduction-valence band coupling in this class of semi-conductors induces a strong mixing of the electronic states which requires a theoretical model to properly take into acount these effects. We have used a full 8 x 8 Kane Hamiltonian in order to include the strong admixture and study the set of symetries associated with these electronic states and their angular momentum in this central force problem. As an application, we have calculated the electronic structure in narrow-gap HgCdTe, InSb and CdTe quantum dots.