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Let fn−1(P) denote the number of facets of a polytope P in R n. We show that there exist 0/1 polytopes P with fn−1(P) ≥ cn log 2 n n/2 where c > 0 is an absolute constant. This improves earlier work of Bárány and Pór on a question of Fukuda and Ziegler.

We show that there exist 0/1 polytopes in R n whose number of facets exceeds cn log n n/2 , where c > 0 is an absolute constant.

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