  We describe singularities of the convex hull of a generic compact smooth
hypersurface in four-dimensional affine space up to diffeomorphisms. It turns
out there are only two new singularities (in comparison with the previous
dimension case) which appear at separate points of the boundary of the convex
hull and are not removed by a small perturbation of the original hypersurface.
The first singularity does not contain functional, but has at least nine
continuous number invariants. A normal form which does not contain invariants
at all is found for the second singularity.
