2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65545We show that the Holt-Klee conditions are very insufficient for an orientation of the graph of a polytope to be an LP-orientation in the case of the n-cube. We also give a strengthening of the Holt-Klee conditions which is both necessary and sufficient in the case of the crosspolytope.9 pagesCombinatoricsCommutative AlgebraOptimization and Control90C05, 52B05text