MODELS OF ICOSAHEDRAL QUASICRYSTALS FROM 6D LATTICES

摘要

The three existing icosahedral modules, P-, 2F- and I-module, are considered. With a particular choice of acceptance domains (vertex-windows), and the coding polytopes for the tiles (windows for the tiles), we define two canonical icosahedrally projected tilings T and T* for each module. In the particular case of the 2F-module all known icosahedral tilings constructed by the process of inflation can be derived from the canonical tilings T'2F' and T*2F and reinterpreted as tilings obtained by icosahedral projection from holes or lattice points of the 6D lattice D6.