  In this pedagogical paper we review the discrete symmetries of the Dirac
equation using elementary tools, but in a comparative order: the usual 3 + 1
dimensional case and the 2 + 1 dimensional case. Motivated by new applications
of the 2d Dirac equation in condensed matter, we further analyze the discrete
symmetries of a full tight-binding model in hexagonal lattices without conical
approximations. We touch upon an effective CPT symmetry breaking that occurs
when deformations and second-neighbor corrections are considered.
