  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.
