  The convex hull peeling of a point set is obtained by taking the convex hull
of the set and repeating iteratively the operation on the interior points until
no point remains. The boundary of each hull is called a layer. We study the
number of k-dimensional faces and the outer defect intrinsic volumes of the
first layers of the convex hull peeling of a homogeneous Poisson point process
in the unit ball whose intensity goes to infinity. More precisely we provide
asymptotic limits for their expectation and variance as well as a central limit
theorem. In particular, the growth rates do not depend on the layer.
