We present a specific geometric description of the approximant phases in quasicrystals using a classification based on symmetry arguments. We derive the 'shear' technique as a special case of this description and discuss the cases of periodic approximants. Observing that all presently known approximant phases have high point symmetry, we make the conjecture that these phases are stabilized by a 'lock-in'-like phenomenon based on maximizing the number of easy atom flips.
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Gratias et al. (1995) studied this question.
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