Algorithms classify rational polygons with a fixed denominator and few interior lattice points, suggesting new identification methods.
We present algorithms for classifying rational polygons with fixed denominator and number of interior lattice points. Our approach is to first describe maximal polygons and then compute all subpolygons, where we eliminate redundancy by a suitable normal form. Executing our classification, we obtained a dataset of several billions of polygons covering a wide variety of cases.
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Bohnert et al. (2026) studied this question.
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