This paper is dedicated to a lattice analog to the classical “sum of interior angles of a polygon theorem”. In 2008, the first formula expressing conditions on the geometric continued fractions for lattice angles of triangles was derived, while the cases of n -gons for n > 3 remained unresolved. In this paper, we provide the complete solution for all integer n . The main results are based on recent advances in geometry of continued fractions.
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Dolan et al. (2025) studied this question.
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