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  "body": "\n## Summary\n\nLet $S$ be a discrete set of points in $\\R^n$.\nThe Voronoi cell of $p \\in S$ is the set of points that are no farther from $p$ than from any other point of $S$.\nThe Voronoi cells of the points of $S$ cover space and meet only along their boundaries.\nFor a [[lattice|WN9V7WSJKF]], all cells are translates of the cell of the origin.\nThis cell is a centrally symmetric convex polytope whose volume is the covolume of the lattice.\nVoronoi cells of lattices are central in lattice packing and covering, in quantization and in decoding.\n\n## Explanations\n\n### L1 human\n\nImagine post offices at the points of $S$, and let everyone go to the nearest post office.\nThe Voronoi cell of a post office is the region of people who go to it.\nFor the integer grid $\\Z^2$, the cell of the origin is the square of side $1$ centred at the origin.\nFor the hexagonal grid of a honeycomb, each cell is a regular hexagon.\n",
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