Prolegomena of quasicrystals

The first published observations of quasicrystals in metallic alloys were in harmony with the increasing complexity of the structural description of possible solid phases, due to specific properties of the magnetic and electric charges of electrons. This led to the complex crystal phases of Frank and Kasper and Meyerʼs prediction of quasicrystalline structures with original diffraction properties in the reciprocal space and local symmetries not allowed for crystals. The initial works on two-dimensional tilings by Penrose and others clarified the problems involved.