A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n = 3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A lattice n-gon in the plane can be equiangular to a regular polygon only for n = 4 and 8. Maehara presented a necessary and sufficient condition for a polygon to be angle-equivalent to a lattice polygon in R^n. In addition, Maehara proved that cos^2( sum_(θ element S) θ) is a rational number for any collection S of interior angles of a lattice polygon.
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