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Livshyts","submitted_at":"2014-09-15T21:19:55Z","abstract_excerpt":"It was shown in \\cite{GL} that the maximal surface area of a convex set in $\\mathbb{R}^n$ with respect to a rotation invariant log-concave probability measure $\\gamma$ is of order $\\frac{\\sqrt{n}}{\\sqrt[4]{Var|X|} \\sqrt{\\mathbb{E}|X|}}$, where $X$ is a random vector in $\\mathbb{R}^n$ distributed with respect to $\\gamma$. In the present paper we discuss surface area of convex polytopes $P_K$ with $K$ facets. We find tight bounds on the maximal surface area of $P_K$ in terms of $K$. 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