By Peter Kramer, Zorka Papadopolos

During this up to date assessment and consultant to latest literature, the specialist authors advance suggestions regarding quasiperiodic coverings and describe effects. The textual content describes particular structures in 2 and three dimensions with many illustrations, and analyzes the atomic positions in quasicrystals.

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325%) of B clusters have no adjacent M clusters. A similar analysis leads to the conclusion that M clusters have unique conM = 7 intersecting B clusters distributed in the same way ﬁguration, with Z¯B as the atoms of the M dodecahedron with the conﬁguration of multiplicity 60 (mirror symmetry) shown in Fig. 15b. This conﬁguration corresponds to 5 B clusters distributed on a pentagon and two out of the plane (like a “stone thrower used as weapon in Roman times”). 764) adjacent B clusters. There are two major conﬁgurations with same frequency, one with 12 neighboring B clusters and the other with 8.

The polyhedron An is the same object but truncated along the 5-fold directions in order to remove too short distances that are too short along these directions. The last polyhedron is Abc and is a triacontahedron obtained by a τ − 1 linear scaling of the canonical triacontahedron. The Wyckoﬀ position bc is empty. A convenient way of showing what kind of order is generated in E by this set of ASs is to draw the rational 2D cuts corresponding to 5-, 3-, and 2-fold directions. In Fig. 5, each 2D map displays the trace of E as a horizontal line and E⊥ as an vertical line: the ASs appear as vertical segments.

17]. 840), where 60∗ refers to a deformed truncated icosahedron. The 12-shell and 20-shell correspond to an icosahedron and a dodecahedron, respectively. If reduced to the ﬁrst four shells, a similar cluster centered on the bcc lattice of the R-phase completely ﬁlls the structure, as shown in [17]. It was then argued that the same cluster could be involved in the structure of the stable i-AlCuLi phase [27] and possibly in other icosahedral phases such as i-AlCuFe and i-AlPdMn. The Mackay cluster (M ) (see Fig.