The reciprocal lattice is frequently generated as a by‐product of the direct lattice or as a convenient abstraction which satisfies the Laue equations. The dualistic point of view from projective geometry is invoked to characterize the information contained in the reciprocal lattice more precisely. From this point of view the reciprocal lattice is seen as an alternate and equally complete representation of the geometric structure of crystal systems. The Ewald and Bragg constructions are displayed as symmetric constructions in their respective lattices.