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 formula_26, where the formula_27 are integers defining the vertex and the formula_28 are linearly independent primitive vectors characteristic of the lattice. There is then a unique plane wave (up to a factor of negative one), whose wavefront through the origin contains the direct lattice points at formula_29 and formula_30, and with its adjacent wavefront passing through formula_31. Its angular wavevector takes the form formula_32, where formula_33 is the unit vector perpendicular to these two wavefronts and the wavelength formula_34 must satisfy formula_35. Hence by construction formula_36 and formula_37.