Approximate isoperimetry for convex polytopes

Keith Ball, Károly J. Böröczky, Assaf Naor

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