We describe an algorithm for classifying and listing all possible hexagonal lattices into which a 2D system can crystallize, in the context of a simulation using periodic boundary conditions. The probability that a system will form one of these lattices depends on its strain energy, but also on the kinetics of nucleation-a crystal must become infinite in one direction before the others. The probability of a given lattice depends on the strain energy of this intermediate state, which we also calculate. The method is applied in an accompanying paper to the taxonomy of hexagonal string lattices that form in sheared colloids.