Voronoi cell

Summary

Let $S$ be a discrete set of points in $\R^n$. The Voronoi cell of $p \in S$ is the set of points that are no farther from $p$ than from any other point of $S$. The Voronoi cells of the points of $S$ cover space and meet only along their boundaries. For a lattice, all cells are translates of the cell of the origin. This cell is a centrally symmetric convex polytope whose volume is the covolume of the lattice. Voronoi cells of lattices are central in lattice packing and covering, in quantization and in decoding.