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VOLUME 67 (1998) | ISSUE 8 | PAGE 557
The electronic spectrum of the three-dimensional quasicrystal
PACS: 71.23.Ft
The electronic spectrum of the icosahedral quasicrystal with a central atom decoration of Amman Mackay network is investigated in the tight binding approximation. The quasicrystal is described as a structural limit of the optimal cubic approximants with increasing period. The electronic spectra for the first four optimal cubic approximants do not contain the hierarchical gap structure which is typical for Cantor set of the spectrum of one-dimensional quasicrystal. At the same time the spectrum with the increase of the order of approximant becomes singular in the whole energy scale.