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Frieze patterns and aperiodic tilings of the plane

2026/07/23 by Dirk Frettlöh, Jan Mazáč
#math.CO #math.MG

paper · pdf

Abstract

This short note provides two examples of aperiodic frieze patterns of the plane, supported on the rhombic Penrose tiling and the Godrèche--Lançon--Billard tiling. That is, we provide a decoration of their vertices with positive integers which satisfy the diamond rule, in analogy to the usual (in)finite frieze patterns as defined by Conway and Coxeter.

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