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  "body": "\n## Definition\n\nA *lattice polytope* in $\\R^n$ is a [[convex polytope|300K6CB1KH]] $P \\subseteq \\R^n$ all of whose [[vertices|R7V3S9V891]] lie in $\\Z^n$.\nEquivalently, $P$ is the convex hull of a finite subset of $\\Z^n$.\n\n## Remarks\n\nExample: the triangle with vertices $(0,0)$, $(3,0)$, $(0,2)$ is a lattice polygon, since all three vertices have integer coordinates.\n\nNon-example: the triangle with vertices $(0,0)$, $(1,0)$, $(0, 1/2)$ is not a lattice polygon, since the vertex $(0, 1/2)$ is not in $\\Z^2$.\nIt is a rational polytope: its vertices lie in $\\Q^2$.\n\nMore generally, for a [[lattice|WN9V7WSJKF]] $\\Lambda \\subseteq \\R^n$, a lattice polytope with respect to $\\Lambda$ is a convex polytope with all vertices in $\\Lambda$.\nA linear change of coordinates turns $\\Lambda$ into $\\Z^n$, so the case $\\Lambda = \\Z^n$ is the standard one.\nTwo lattice polytopes are usually regarded as the same when an affine map $x \\mapsto Ax + b$ with $A \\in GL_n(\\Z)$ and $b \\in \\Z^n$ carries one onto the other.\n",
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