Abstract
After an introductory survey, a recent development in the theory of quasicrystal-related four-coordinated structures is presented. Two crystalline approximants, 1/0 (known as the BC8 phase) and 1/1, are studied in detail. A novel method for construction of four-coordinated structures from the Frank-Kasper dense-packed systems is suggested and several new structures are constructed. The energies of those structures and topological phason disorder are studied ab initio.
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