The split closure of a strictly convex body

The Chvátal–Gomory closure and the split closure of a rational polyhedron are rational polyhedra. It has been recently shown that the Chvátal–Gomory closure of a strictly convex body is also a rational polytope. In this note, we show that the split closure of a strictly convex body is defined by a finite number of split disjunctions, but is not necessarily polyhedral. We also give a closed form expression in the original variable space of a split cut for full-dimensional ellipsoids.