Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some potentials that do not satisfy them are discussed. It is shown that in addition to the triangular lattice, other structures may appear (some of them with nontrivial unit cells, and nonequivalent positions of the particles) even for simple choices of the interaction. The same qualitative behavior is expected in three dimensions.