Two distinct points and different from the origin define a lattice, the set of points .

The polygon can be translated by one of the lattice points. If the translates cover the plane without overlapping, they are said to tile the plane. If each point of the plane is covered exactly times, the polygons are said to -tile the plane.

In this Demonstration, drag the locators to define the endpoints of segments from the origin. The Minkowski sum of a set of segments is a convex polygon. Choose a tiling lattice; the polygon is translated by points of the lattice, centered at the origin. A consistent shading in the graphic indicates a -tiling.