Dihedral flavor symmetry from dimensional deconstruction

Extra dimension deconstructed on a closed chain has naturally the symmetry of a regular polygon, the dihedral symmetry DN. We assume that the fields are irreducible representations of the binary dihedral group Q2N, which is the covering group of DN. It is found that although the orbifold boundary conditions break the dihedral invariance explicitly, the Q2N symmetry appears as an intact, internal global flavor symmetry at low energies. A concrete predictive model based on Q6N with an odd N is given.