Quasicrystal structure analysis, a never-ending story?

Quasicrystal structure analysis comprises the determination on an atomic scale of both the short-range order (SRO) and long-range-order (LRO). SRO mainly refers to the atomic arrangement inside a cluster (i.e. a recurrent structural building unit), LRO to the ordering of the clusters themselves. The LRO of periodic structures can definitely be described by one of the 14 Bravais lattice types. In the case of quasicrystals, there is a choice of infinitely many different strictly quasiperiodic atomic arrangements, not to mention other types of aperiodic structures. Consequently, due to limited experimental information quasicrystal structures can only be solved approximately. In the case of a few decagonal and icosahedral phases the combined effort of mainly electron microscopic and diffraction methods conveyed an idea about the structure of clusters and their way of long-range ordering. However, we are still far away from the type of quantitative structure analysis as a function of temperature and pressure needed to answer the fundamental questions about the formation, structure and stability of quasicrystals.