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The decrease of symmetry occurring when the six-dimensional icosahedral lattice is deformed is discussed. For certain deformations a periodic instead of a quasi-periodic structure may appear. As examples transitions to tetrahedral and rhombohedral crystal phases are considered. In particular for the rhombohedral case the transition may go via a modulated quasi-crystalline phase, as has been observed recently. A possible transition scheme is proposed and the character of the atom displacements is shown in that case.
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Τ. Janssen (1991) studied this question.
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