One heuristic approach to constructing the reciprocal lattice in three dimensions is to write the position vector of a vertex of the direct lattice as R = n 1 a 1 + n 2 a 2 + n 3 a 3 , where the n i are integers defining the vertex and the a i are linearly independent primitive translation vectors (or shortly called primitive vectors) that are characteristic of the lattice. There is then a unique plane wave (up to a factor of negative one), whose wavefront through the origin R = 0 contains the direct lattice points at a 2 and a 3 , and with its adjacent wavefront (whose phase differs by 2 π π or − − 2 π π from the former wavefront passing the origin) passing through a 1 . Its angular wavevector takes the form b 1 = 2 π π e 1 / λ λ 1 , where e 1 is the unit vector perpendicular to these two adjacent wavefronts and the wavelength λ λ 1 must satisfy λ λ 1 = a 1 ⋅ ⋅ e 1 , means that λ λ 1 is equal to the distance between the two wavefronts. Hence by construction a 1 ⋅ ⋅ b 1 = 2 π π and a 2 ⋅ ⋅ b 1 = a 3 ⋅ ⋅ b 1 = 0 .