A Latin square is an n × n matrix where in each row and each column every number between 1 and n appears exactly once. A Latin square can be described by a binary vector with n 3 components, and the Latin square polytope (P n;I) is the convex hull of such binary vectors. We study the facial structure of P n;I by examining valid inequalities induced by the odd holes of the associated intersection graph. In particular, we define the concept of the lifting set of an odd hole, present an efficient algorithm for identifying it and derive tight bounds on the left-hand side coefficients of an induced odd-hole inequality. In this way, we are able to characterize the class of odd holes that yield maximal inequalities without lifting and show that, for sufficiently large n, they are facet-defining for P n;I. This outcome unifies and generalizes previous results, with respect to the classes of facets for P n;I, presented in the literature. Computational experience regarding the use of (lifted) odd-hole inequalities as cutting planes is reported.