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Figure 10
The complete set of Φ-lattices for the octagonal (a) and dodecagonal (b) quasiperiodic patterns (see Fig. 11[link] for a general discussion). In these high-symmetry cases, the prefactors [A_{\Phi}] and thus the a unit-cell vectors of the corresponding Φ-lattice (with [t_{\Phi} = \tau = 0]) are all half an integer sum of a node of L1 with a node of L2.

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