In this paper we examine the detailed relationship between the density-wave and unit-cell descriptions of quasicrystals. We show that phonons, phasons, and dislocations correspond to translations, distortions, and rearrangements of unit cells. The associated density-wave images closely resemble experimental electron micrographs of the icosahedral phase of aluminum-manganese and related alloys. Partial dislocations are also discussed and a natural classification scheme for partials is proposed.
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Socolar et al. (1986) studied this question.
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