An analytical relationship is found between triple correlations and nearest neighbor pair correlations in an AyB1 – y solid solution with a planar hexagonal lattice (plane group p6mm). The range of variations in the triple correlation is determined as a function of the composition of the AyB1 – y solid solution and the value of the pair correlation. It is assumed that periodically ordered planar hexagonal and square island nanostructures can be considered as solid solutions A1/4 3/4 with vacancy sites and sites occupied by nanoparticles A. In this case, an ordered distribution of nanoparticles over the planar-lattice sites occurs because the nearest neighbor pair correlation is negative and has a maximum magnitude.