Nonclassical plane-crystallographic groups and their applications IV

Eight kinds of nonclassical periodic lattices with locally 8-fold rotational symmetries are introduced. They can be described via nonclassical Plane-crystallographic groups. The periodic lattices may be interpreted by the projections on the plane of the corresponding unit cells consisting of embedding polyhedrons, respectively. The Fourier-transform patterns of the periodic lattices have striking. approximate "8-fold rotational symmetries", some of which are similar to those displaying in the electron-diffraction patterns of so-called quasicrystalls.