A global cut-and-project method is developed. By this technique, the construction is discussed of aperiodic lattices including both generalized Fibonacci lattices and octagonal, decagonal and dodecagonal quasilattices. Diffraction patterns with 8-, 10-, and 12-fold symmetries are simulated, which agree well with the experimental results. A modulation is introduced to explain the two alternating sets of periodic layers along the 10-fold axis in the diffraction pattern of decagonal quasicrystal.
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