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  "body": "\n## Summary\n\nPolytope combinatorics, also called polyhedral combinatorics, studies convex polytopes through their faces.\nIt asks how many faces of each dimension a polytope has and how the faces fit together.\nIts typical questions ask which [[f-vectors|DCK64GFPD7]] are possible, as in [[Euler's polyhedron formula|09HT3P35YP]], the [[Dehn–Sommerville equations|4WKHF5BCTA]] and the [[g-theorem|4CZMWQVC30]].\nThe same name covers the study of the facets of polytopes defined by combinatorial optimization problems, a tool of integer programming.\n\n## Explanations\n\n### L1 human\n\nA cube has $8$ vertices, $12$ edges and $6$ square faces, and any squashed cube with flat faces has the same pattern.\nPolytope combinatorics forgets lengths and angles and keeps only this pattern of vertices, edges and faces.\nIt asks, for example, which lists of face numbers can occur, and in every dimension, not only in three.\n",
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