A polygon whose vertices are points of a point lattice. Regular lattice -gons exists only for , 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963,
Maehara 1993). A lattice -gon in the plane can be equiangular to a regular polygon only
for
and 8 (Scott 1987, Maehara 1993).

Maehara (1993) presented a necessary and sufficient condition for a polygon to be angle-equivalent to a lattice polygon in . In addition, Maehara (1993) proved that is a rational
number for any collection of interior angles of a lattice polygon.

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I. "Size and Area of Square Lattice Polygons." 28 Mar 2000. http://arxiv.org/abs/cond-mat/0003442.Klamkin,
M. and Chrestenson, H. E. "Polygon Imbedded in a Lattice." Amer.
Math. Monthly70, 51-61, 1963.Maehara, H. "Angles in
Lattice Polygons." Ryukyu Math. J.6, 9-19, 1993.Schoenberg,
I. J. "Regular Simplices and Quadratic Forms." J. London Math.
Soc.12, 48-55, 1937.Scott, P. R. "Equiangular
Lattice Polygons and Semiregular Lattice Polyhedra." College Math. J.18,
300-306, 1987.