Group theory considerations in quasicrystal to crystal transformations

摘要

We first discuss several aspects of group theory for reformulating the group-subgroup relations in quasicrystals to crystals transformations based on the original approach proposed by D. Mermin and his group on indiscernability groups. In the second part of the paper, we discuss ways of determining the possible space-groups of approximants of quasicrystals as generated by the perpendicular shear technique.