Abstract: The diffraction formula of a kind of lattice of points with 12-fold symmetry is deduced. The optical transform of the lattice of points is made. By different ratio of the reciprocal lattice, several diffraction patterns are drawn through eliminating the diffraction spots of different intensities. One of the patterns agrees with the optical transform of the lattice of points andis approximate the diffraction pattern of Ni-based superalloy and another patternis approximateo the diffraction pattern of quasicrystal with 12-fold symmetry. The possibility that ‘quasicrystals with 5-fold, 8-fold, 10-fold and 12-fold symmetry’ may be in fact periodic structures should not be excluded.