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Enumerating lattice points in rational polytopes

Is there a way to ask Sage to count the number of lattice points in a rational polytope, say a polytope with vertices (0,0,0,0), (0,0,0,7), (0,0,7/2,7/2), (0,7/3,7/3,7/3),(7/4,7/4,7/4,7/4)?