A polygon whose interior consists of all points in the plane which are closer to a particular lattice point
than to any other. The generalization to 
dimensions is called a Dirichlet region, Thiessen polytope,
or Voronoi cell.
Voronoi Polygon
See also
Voronoi DiagramExplore with Wolfram|Alpha
References
Dirichlet, G. L. "Über die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen." J. reine angew. Math. 40, 209-227, 1850.Voronoi, G. "Recherches sur les paralléloèdres Primitives." J. reine angew. Math. 134, 198-287, 1908.Williams, R. The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover, p. 43, 1979.Referenced on Wolfram|Alpha
Voronoi PolygonCite this as:
Weisstein, Eric W. "Voronoi Polygon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VoronoiPolygon.html