The results of a theoretical study of the nanostructured ternary compound HAIO are presented. We have considered isolated (HAIO), clusters, the interactions between two such clusters, and two-dimensional layers of HAIO. In many of the calculations we used a parametrized density-functional tight-binding method in the calculation of the electronic properties for a given structure, combined with two different unbiased approaches, i.e., an "Aufbau" and a genetic-algorithm method, for optimizing the structure for clusters with n up to 26. The results for the isolated clusters are analyzed by means of similarity, stability, and shape parameters. Isolated structures with it up to 6 were also studied intensively with pure DFT methods.