AbstractThe beautiful external forms of crystals are manifestations of their internal structures. These structures, which can be regarded as infinite periodic patterns, are determined by local forces. In this article we discuss symmetry from the “local” point of view. First we show that the symmetry of an infinite regular point set (the atomic pattern of an ideal crystal) is a consequence of the symmetry of finite configurations in the pattern. Then we briefly discuss the basic structural feature of internal crystal symmetry, the space lattice, and its relation to the crystal's external form. This form is predicted by locally defined growth rules. We conclude with an open problem, the origin of the symmetry and form of crystal twins.