DENSE QUASI-PERIODIC DECAGONAL DISC PACKING

An inflation rule is given which proves the existence of infinite decagonal rectangle-triangle tilings. Such tilings correspond to the maximum possible density of a decagonal disc packing and can be used to model decagonal quasicrystals. A lower bound 0.0336 per vertex is found for the entropy density of the corresponding random-tiling system. The atomic surfaces for a deterministric version of the packing are self-similar and disconnected. The relationship between rectangle-triangle tilings and real decagonal phases is discussed. It is shown that the large unit cell associated with observed microcrystalline phases has a natural explanation in the context of rectangle-triangle tilings. © 1995 The American Physical Society.