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  "body": "\n## Summary\n\nThe f-vector of a [[convex polytope|300K6CB1KH]] lists how many faces it has in each dimension.\nFor a $d$-polytope it is $(f_0, f_1, \\dots, f_{d-1})$, where $f_i$ is the number of $i$-dimensional faces.\nThe same notion applies to [[simplicial complexes|V8GZ0W1ZZ5]], and it is the starting point for the h-vector; see [[f-vector and h-vector|DCK64GFPD7]].\nDescribing which vectors are f-vectors is a main problem of [[polytope combinatorics|879SBTVE7V]].\n\n## Explanations\n\n### L1 human\n\nCount the corners, edges, faces and so on of a shape, and write the counts in a row.\nThat row is the f-vector.\nA cube gives $(8, 12, 6)$: $8$ corners, $12$ edges and $6$ square faces.\nThe numbers in an f-vector are not arbitrary; for solids in space the corners minus edges plus faces is always $2$.\n",
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