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Infinite friezes
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We provide a characterization of infinite frieze patterns of positive integers via triangulations of an infinite strip in the plane. In the periodic case, these triangulations may be considered as triangulations of annuli. We also give a geometric interpretation of all entries of infinite friezes via matching numbers.
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Frieze patterns and aperiodic tilings of the plane
Penrose rhombic tilings admit a four-valued vertex frieze pattern and Godrèche–Lançon–Billard tilings admit a three-valued one, both satisfying the diamond rule bc−ad=1.
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