Sequences of clusters with a short-range interaction of atoms which form symmetrical structures are constructed. Expressions for cluster parameters of some sequences at zero temperature are obtained within the framework of a general scheme. Distributions of atoms on cluster shells at finite temperatures are evaluated. An analysis sets up a correspondence between parameters of large clusters and macroscopic particles or macroscopic surfaces. The nature of the solid-liquid phase transition for clusters and other systems of atoms with a short-range interaction is discussed.