Free and ligated oxide clusters of thorium(IV) and uranium(IV) were studied with density functional theory using all-electron scalar relativistic method, as well as energy-consistent relativistic f-in-core pseudopotentials. The main driving force for the cluster formation is the sintering of the dioxoactinide moieties, which is more favorable for thorium(IV) than for uranium(IV) because, for the latter, a penalty for bending of the uranyl(IV) is to be paid. We assumed that the rhombic structural motif that exists already in the (AnO(2))(2) dimer could be a guide to explaining the preference for the existing An(6)O(8)-type clusters. On the basis of this, we have theoretically explored the possibility of the existence of similar (zonohedric) polyhedral actinide oxide clusters and found that the next possible cluster would be of An(12)O(20) stoicheometry. We have predicted by our DFT computations that the corresponding zonohedral clusters would be minima on the potential energy surface. The alternating An-O rhombic structural motif also offers a possible explanation of the existence and stoichiometry of the only nonfluorite cluster thus far, the An(12)O(20), which is nonzonohedral, nonconvex, but still a rhombic polyhedron. Our relativistic all electron DFT computations of both free cationic and ligated clusters predict that preparation of the larger clusters is not forbidden thermodynamically. We have also found that for the uranium(IV), oxide dimer and hexamer clusters are antiferromagnetic, broken spin singlet in their ground state, while ligated [U6O8] clusters prefer an all high-spin electronic configuration.