Cycling through the indices in turn, the same method yields three wavevectors b j with a i ⋅ ⋅ b j = 2 π π δ δ i j , where the Kronecker delta δ δ i j equals one when i = j and is zero otherwise. The b j comprise a set of three primitive wavevectors or three primitive translation vectors for the reciprocal lattice, each of whose vertices takes the form G = m 1 b 1 + m 2 b 2 + m 3 b 3 , where the m j are integers. The reciprocal lattice is also a Bravais lattice as it is formed by integer combinations of the primitive vectors, that are b 1 , b 2 , and b 3 in this case. Simple algebra then shows that, for any plane wave with a wavevector G on the reciprocal lattice, the total phase shift G ⋅ ⋅ R between the origin and any point R on the direct lattice is a multiple of 2 π π (that can be possibly zero if the multiplier is zero), so the phase of the plane wave with G will essentially be equal for every direct lattice vertex, in conformity with the reciprocal lattice definition above. (Although any wavevector G 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.)