Formulae expressing the amplitude for a Feynman diagram consisting of a single internal loop withn sides andn external lines as a sum of its reduced diagrams are derived by applying restrictions imposed by the finite dimensionality of space-time on the unparametrized amplitude. In 4-dimensional space-time these formulae express the amplitude for then-sided diagram as i) a sum of all its 5-sided reduced diagrams; this can be further expressed as ii) a sum of all its 4-sided reduced diagrams. The coefficients in each sum depend only on the external invariants and internal masses.