Structural features of quasicrystals and their electronic states for two- and three-dimensional cases

Abstract The grid dual to Penrose lattice is shown to be obtained from a crystal by applying successive periodic modulations, which have the periods 3, 3 2 , 3 3 , …, both in the x- and y-directions. The electronic states on the grid are discussed and the distribution of the level spacing is shown to be in good agreement with numerical work.