English: An example showing the increased power of Blichfeldt's theorem over Minkowski's theorem for finding lattice points in non-convex sets. The (closed) yellow set ${\displaystyle Y}$ on the left has area 1, so by Blichfeldt's theorem it can be translated to cover two points of any lattice whose fundamental region has volume 1, such as the red lattice. It follows that the blue set ${\displaystyle X=Y-Y}$ on the left, the set of differences of pairs of points in ${\displaystyle Y}$, when centered on a lattice point, also contains at least one other lattice point as well as the center. In contrast, the blue rectangle ${\displaystyle R}$ on the right, the largest convex subset of ${\displaystyle X}$, has too small an area for Minkowski's theorem to guarantee that it contains another lattice point, and the smaller yellow rectangle ${\displaystyle {\tfrac {1}{2}}R}$ within it is too small to apply Blichfeldt's theorem.