The two-dimensional square lattice has ai ae, and a2 aéz. 1. show that the reciprocal lattice is also square. 2. use the following recipe for finding the first three brillouin zones: the b8z is obtained by starting at any reciprocal lattice point (which is then the origin) and constructing vectors to all neighbouring reciprocal lattice points. lines are then constructed perpendicular to and passing through the midpoints of these vectors. the bz is the cell with the smallest area about the origin bounded by these lines. the 2nd b2 is the area between the 1t bz and the next smallest closed polygon formed by the lines. similarly for the 3" bz.