Modeling of dodecagonal quasicrystal lattices

Abstract

We consider a method for constructing dodecagonal quasi-lattices, which involves the recurrent multiplication of the initial group of sites that are vertices of a regular dodecagon. The algorithm of modeling of reciprocal lattices of dodecagonal quasicrystals has been analyzed. The proposed modeling method is compared with the traditional projection method. We have performed indexing of the diffraction pattern from dodecagonal quasicrystals, which is analogous to indexing proposed by Cahn for icosahedral quasicrystals. The ambiguity of the choice of the basis vectors of the quasicrystal reciprocal lattice has been considered.