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It is shown that the icosahedral quasicrystal and the recently observed T phase are closely related to each other. The latter is a periodic stacking of two-dimensional quasilattices with mirror symmetry. Their diffraction patterns, though appearing very different, can be indexed by a set of primary vectors that are only small deformations of each other. However, because of the mirror symmetry, their quasilattices are not related by small deformations. A calculation based on the model free energy of Kalugin et al. shows that this periodic quasicrystal is very competitive with (and in fact energetically more favorable than) the icosahedral quasicrystal.
Tin-Lun Ho (Mon,) studied this question.