Approximate isoperimetry for convex polytopes

Keith Ball, Károly J. Böröczky, Assaf Naor

For all $n,\varphi \in \mathbb{N}$ with $\varphi ⩾n+1$, the smallest possible isoperimetric quotient of an $n$-dimensional convex polytope that has $\varphi$ facets is shown to be bounded fro…