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We consider mixed integer linear programs where free integer variables areexpressed in terms of nonnegative continuous variables. When this model onlyhas two integer variables, Dey and Louveaux characterized the intersection cutsthat have infinite split rank. We show that, for any number of integervariables, the split rank of an intersection cut generated from a boundedconvex set $P$ is finite if and only if the integer points on the boundary of$P$ satisfy a certain "2-hyperplane property". The Dey-Louveauxcharacterization is a consequence of this more general result.

Intersection Cuts with Infinite Split Rank