A convex body with chaotic random convex hull

The asymptotic behavior of the size of the convex hull of uniformly random points in a convex body in Rd is known for polytopes and smooth convex bodies. These are the lower and the upper bound for a general convex body. In this paper, we exhibit an example of convex body whose size of the random convex hull alternates behavior close to the lower and to the upper bound for some values of the number of points arbitrary big.