Estimates for the minimal width of polytopes inscribed in convex bodies (Q583611)

For a given family \({\mathcal A}\) of convex bodies in d-dimensional Euclidean space, let \(\Lambda_ n({\mathcal A})\) be the greatest number \(\mu\) such that every set \(A\in {\mathcal A}\) contains a polytope P with at most n vertices such that w(P)\(\geq \mu w(A)\). Here w denotes the minimal width and \(n\geq d+1\) is a given integer. The authors take for \({\mathcal A}\) the classes of all convex bodies, centrally symmetric bodies, or bodies of constant width, and they obtain lower bounds for \(\Lambda_ n({\mathcal A})\) as well as explicit values in special cases.