Cluster coverings as an ordering principle for quasicrystals

Cluster density maximization and (maximal) cluster covering have emerged as ordering principles for quasicrystalline structures. The concepts behind t hese ordering principles are reviewed and illustrated with several examples . For two examples, Gummelt's aperiodic decagon model and a cluster model f or octagonal Mn-Si-Al quasicrystals, these ordering principles can enforce perfectly ordered, quasiperiodic structures. For a further example, the Tub ingen triangle tiling (TTT), the cluster covering principle fails to enforc e quasiperiodicity, which sheds some light on the limitations of this appro ach. (C) 2000 Elsevier Science B.V. All rights reserved.