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Dec 27, 2021 at 9:33 comment added dohmatob Thanks. For the record, if $f_k(P)$ is the number of $k$-dimensional faces of $P$, then the referenced Dehn-Sommerville equations (combined with Upper Bound Theorem) yield $f_{d-1}(P) \le 2{n-(d+1)/2 \choose n-d}$.
Dec 27, 2021 at 9:30 vote accept dohmatob
Dec 27, 2021 at 8:56 history answered Tony Huynh CC BY-SA 4.0