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Figure 1
Passing from monolayer I to monolayer II is achieved by the set [\widehat{{\boldalpha}}_{\tau}{\cal G}] and from II to I by the inverse set [{\cal G}\widehat{{\boldalpha}}_{\tau}^{-1}]. The overlap of the monolayers, designed here as a bilayer, generates its own symmetry that is a 2D space group if the two lattices Λ and [\Lambda^{\prime}] have a common coincidence lattice [{\cal T} = \Lambda\cap\Lambda^{\prime}] and only a quasiperiodic symmetry otherwise.

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