Dihedral Flavor Symmetry from Dimensional Deconstruction

Extra dimension deconstructed on a closed chain has naturally the symmetry of a regular polygon, the dihedral symmetry D_N. We assume that the fields are irreducible representations of the binary dihedral group Q_2N, which is the covering group of D_N. It is found that although the orbifold boundary conditions break the dihedral invariance explicitly, the Q_2N symmetry appears as an intact internal, global flavor symmetry at low energies. A concrete predictive model based on Q_6N$ with an odd N is given.