  We address the question of whether three-dimensional crystals are minimizers
of classical many-body energies. This problem is of conceptual relevance as it
presents a significant milestone towards understanding, on the atomistic level,
phenomena such as melting or plastic behavior. We characterize a set of
rotation- and translation-invariant two- and three-body energies such that the
energy minimum per particle over all n-particle configurations converges to the
energy per particle in the face-centered cubic (fcc) lattice as tends to
infinity. The proof involves a careful analysis of the symmetry properties of
the fcc lattice.
