Cycling through the indices in turn, the same method yields three wavevectors formula_38 with formula_39, where the Kronecker delta formula_40 equals one when formula_41 and is zero otherwise. The formula_38 comprise a set of three primitive wavevectors for the reciprocal lattice, each of whose vertices takes the form formula_43, where the formula_44 are integers. Simple algebra then shows that, for any plane wave with wavevector formula_45 on the reciprocal lattice, the total phase shift formula_46 between the origin and any point formula_47 on the direct lattice is a (possibly zero) multiple of formula_48, so the phase will indeed be equal for every direct lattice vertex, in conformity with the reciprocal lattice definition above. (Although any wavevector formula_45 on the reciprocal lattice does always take this form, this derivation is motivational, rather than rigorous, because it has omitted the proof that no other possibilities exist.)