Superquasicrystals with 8-, 10- and 12-fold point symmetries

Abstract

We present several limit-quasiperiodic structures with 8-, 10- and 12-fold point symmetries. These structures are generated with inflation procedures as in the case of the Penrose patterns. Yet they are the first structures ever known with limit-quasiperiodic order and non-crystallographic point symmetries, and we categorize them as superquasicrystals [Niizeki and Fujita, J. Phys. A: Math: Gen. 38 L199 (2005)]. Their internal space structures are not as simple as quasicrystals, because the atomic-surfaces depend on the lattice points of the relevant hyperlattices. We numerically investigate such atomic-surfaces by mapping the real-space structure into the internal space. The structure factors are also calculated, in which successive generations of super-quasilattice reflections are clearly observed.