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This paper is an attempt to present a chronological review of the structural concepts that have been developed to characterize quasicrystals, starting from the experimental discovery of D. Shechtman  and the concomitant theoretical definition of quasicrystal as proposed by D. Levine and P. Steinhardt , up to the present research in the field. The largest part of the paper is a discussion of the specific points that make the atomic structure determination of quasicrystals an original anddoi:10.1080/14786430801971474 fatcat:oxbdp5azbjg57gnzh3m5nuq4di