Quasi-crystal structure: cold water on the Penrose tiling scheme

Abstract

Quasi-crystalline structures are related to periodic distributions of A3perp volumes in a higher-dimensional space. If these A3perp volumes are actually confined inside the complementary space, three-dimensional Penrose lattice can be generated by the six-dimensional cut method. Diffraction data show that the actual A3perp must have components in the physical space, which make the three-dimensional structure description in terms of Penrose tiling not really reliable. Such 'parallel' components have been experimentally observed for the first time.