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  "body": "\n## Summary\n\nA lattice polytope, also called an integral polytope, is a [[convex polytope|300K6CB1KH]] whose vertices all have integer coordinates.\nCounting the integer points in such a polytope and in its dilates leads to the [[Ehrhart polynomial|9DEG0WRDHR]].\nLattice polytopes link convex geometry with combinatorics, with integer programming and, through their [[normal fans|XJ83PTS3H0]], with [[toric varieties|YWB981MEF2]].\n\n## Explanations\n\n### L1 human\n\nDraw a square grid of points and join some of the grid points to make a convex shape with straight sides.\nIf every corner of the shape sits on a grid point, the shape is a lattice polygon.\nThe square with corners $(0,0)$, $(2,0)$, $(2,2)$, $(0,2)$ is one; it contains $9$ grid points.\nLattice polytopes are the same idea in any dimension.\n",
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