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We consider the problem of extraction and validation of matching rules, directly from the phased diffraction data of a quasicrystal, and propose an algorithmic procedure to produce the rules of the shortest possible range. We have developed a geometric framework to express such rules together with a homological mechanism enforcing the long-range quasiperiodic order. This mechanism tolerates the presence of defects in a robust way.doi:10.1088/1742-6596/1458/1/012002 fatcat:xgdnybyu55hetgk25jstkrskhe