This paper considers the issues of building a model of the cluster organization of Al2O3 on principles directly associated with the involvement of a non-Euclidian technique of describing. As a modeling space, which most adequately describes the internal structure of a real crystal, a finite closed space with elliptic metric and constant positive Gaussian curvature (K=1) was chosen, which assumes the realization of lattice systems in compliance with Fedorov groups of transformations. An algorithm for generating the cluster structures is presented, which determines the sequence of filling of the model space with cations and anions, taking into account the symmetry of a microstructure (a Fedorov group) and the electrostatic parameters of ions. Calculations of the geometrical sizes of nano- and microcrystalline complexes of Al2O3 are given, taking into account the structural features of their formation at the cluster level. Practical applications connected with improving the structural characteristics of crystalline materials are discussed.