Periodic pentagonal and decagonal quasicrystals

Abstract

A structure with quasiperiodicity in two dimensions and periodicity in the third has been generated by projection from 6D space. The effect of simultaneously distorting along one axis the 6D cubic cell as well as the icosahedron formed by the projection of the 6D unit vectors onto physical space has been examined for the first time. Some examples are considered to illustrate the generation of structures with P5¯mm, P${10}_5$/mcm, and P10/mmm symmetry.