Abstract
AbstractIt is well-known that a regular n-gon can be embedded in the unit lattice of ℝm if and only if m ≥ 2 and n = 4; or m ≥ 3 and n = 3 or 6. In this paper we consider equilateral polygons that can be embedded in the unit lattice of ℝk. These are called lattice equilateral polygons. We show that for any ε > 0, there exists a lattice equilateral 2n-gon in ℝ2 such that the difference between the values of the maximum internal angle and the minimum internal angle is less than ε. We also show a similar result for lattice equilateral 3n-gons in ℝ3 and other related results.KeywordsPositive IntegerLattice PointSimilar TransformationUnit LatticeInternal AngleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Published Version
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