Facet lower bound for ball approximations
= Facet lower bound for ball approximations
{title2=$f_{n-1}(P)\geq e^{n/(2r^2)}$}
If $r\geq\sqrt2$ and a <convex polytope> satisfies $r^{-1}B^n\subseteq P\subseteq B^n$, then it has at least $(1-r^{-2})^{-n/2}\geq e^{n/(2r^2)}$ <facets>. Its outward facet normals define <spherical caps> covering the <unit sphere>; the <spherical cap area upper bound> supplies the estimate.