POSSIBLE 2-DIMENSIONAL QUASI-CRYSTAL STRUCTURES WITH A 6-DIMENSIONAL EMBEDDING SPACE

A discussion is given of all possible two-dimensional (2D) quasicrysta l structures with a six-dimensional (6D) embedding space. Such quasicr ystals have some properties different from the properties of known 2D quasicrystals. It is predicted that the diffraction pattern of the qua sicrystal structures considered here can be indexed with integers usin g six rationally independent reciprocal basis vectors. They have seven -, nine-, fourteen-, and eighteenfold symmetries. The six hydrodynamic degrees of freedom in phases can be parametrized by three two-dimensi onal vector fields, and hence there are two types of phason fields in each case mentioned above. All quadratic invariants and elastic energy densities are also derived for such quasicrystals with use of group-r epresentation theory.