Covering cluster description of octagonal MnSiAl quasicrystals

A likely mechanism far the formation of quasicrystals is by maximally covering space with overlapping, stable atomic clusters. This notion is here applied to the experimentally determined layered structure of octagonal MnSiAl quasicrystals, which can be described in terms of a decoration of the octagonal Ammann-Beenker tiling. This decoration is abstractly represented by a two-color version of the tiling. The covering cluster of the quasicrystal corresponds to an octagonal covering patch of the colored tiling. This covering patch appears, in two variants with complementary colors. The three-dimensional quasicrystal has a centered octagonal translation module, and its space group is 18(4)/mcm.