  We study the origin of non-Abelian discrete flavor symmetries in superstring
theory. We classify all possible non-Abelian discrete flavor symmetries which
can appear in heterotic orbifold models. These symmetries include D_4 and
Delta(54). We find that the symmetries of the couplings are always larger than
the symmetries of the compact space. This is because they are a consequence of
the geometry of the orbifold combined with the space group selection rules of
the string. We also study possible breaking patterns. Our analysis yields a
simple geometric understanding of the realization of non-Abelian flavor
symmetries.
