Nonclassical Periodic Models Fourier Transforms and Group

Three kinds of nonclassical periodic plane-lattices with locally 8-, 10-, and 12-fold symmetry are proposed. they can be interpreted as the projections on the plane of space models consisting of different polyhedra.The Fourier-transform patterns of the space models have approximate 8-, 10-, and 12-fold rotational symmetry which is hardly distinguishable from the corresponding symmetry in the strict mathematical sense and qualitatively similar to the electron-diffraction patterns with 8-,10-, and 12-fold symmetry of corresponding quasicrystals. These lattice can be described by a new "composites" of the traditional translation operations and rotation operations. Nonclassical crystallographic groups are set up.