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  "body": "\n## Summary\n\nA facet of a [[convex polytope|300K6CB1KH]] is a [[face|KY7SB854VH]] of the largest possible dimension below that of the polytope itself.\nA polytope of dimension $d$ has facets of dimension $d - 1$.\nThe facets determine the polytope: a full-dimensional polytope is the intersection of the closed half-spaces bounded by the hyperplanes of its facets.\nCounting facets and studying their shapes is a central theme of [[polytope combinatorics|879SBTVE7V]].\n\n## Explanations\n\n### L1 human\n\nThe facets of a solid are the flat pieces of its surface that are \"one dimension down\".\nFor a cube in space they are the six square faces.\nFor a polygon in the plane they are its edges.\nFor a four-dimensional cube they are eight ordinary cubes.\nEach facet sits on a wall, and the polytope is what lies on the inner side of all the walls.\n",
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