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answered 2017-10-12 08:47:54 +0100
There is
sage: P = Polyhedron([(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)]) sage: P.integral_points_count() 38