Mosaic Structure of Quasicrystals of Three Hexagonal Atomic Layers

A previously unconsidered tiling structure of a quasicrystal mosaic of three hexagonal monolayers with 18-fold rotational symmetry (3QC) when their three lattices are brought together in a plane has been proposed. Three-dimensionality of the tiles in the mosaic picture for van-der-Waals -separated 3QC objects of monoatomic (C, Si, Ge, etc.) lattices leads to a six-fold “color” symmetry included in the 18-fold symmetry of the unseparated lattice model. For 3QC of diatomic (BN, MoS 2 , etc.) lattices, the color mosaic has a three-fold symmetry.