Mean-Width and Diam(K)

Question

I believe the following is always true:

if $A$ is a Convex Hull of some points in $R^n$, then we have

$meanwidth(A)$$\ge$$C$$\cdot$$diam$$(A)$ ; (where the $diam$ stands for the maximum distance between 2 points in the same Convex Hull)

I need the above constant $C$ precisely, but I couldn't find any paper, text, book etc. containing the precise value of $C$. Any ideas?

Answer 1

Hug, Daniel; Weil, Wolfgang, $\textit{A Course on Convex Geometry}$. Very nice book if you are interested in Convex Geometry; explains the above mentioned property.