1 Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan Max-Planck-Institut for Chemical Physics of Solids, 01187 Dresden, Germany 3 Sciences de l’Ingéniérie, des Matériaux et des Procédés, Grenoble INP, CNRS, 28402 cedex, France E-mail: [email protected]. ac.jp The discovery of quasicrystal in 1982 has facilitated a revolution in crystallog...

The mathematical descriptions of quasicrystal' show that for a given quasicrystalline symmetry, there is an uncountably infinite number of distinct packing of unit cells. At present, these packings [different local isomorphism (LI}classes] and the unit-cell decoration cannot be determined simultaneously from diffraction data. Steinhardt and co-workers introduce three criteria for the identifica...