  Recently, several new materials exhibiting massless Dirac fermions have been
proposed. However, many of these do not have the typical graphene honeycomb
lattice, which is often associated with Dirac cones. Here, we present a
classification of these different two-dimensional Dirac systems based on the
space groups, and discuss our findings within the context of a minimal two-band
model. In particular, we show that the emergence of massless Dirac fermions can
be attributed to the mirror symmetries of the materials. Moreover, we uncover
several novel Dirac systems that have up to twelve inequivalent Dirac cones,
and show that these can be realized in (twisted) bilayers. Hereby, we obtain
systems with an emergent SU(2N) valley symmetry with N=1,2,4,6,8,12. Our
results pave the way to engineer different Dirac systems, besides providing a
simple and unified description of materials ranging from square- and
$\beta$-graphynes, to Pmmn-Boron, TiB$_2$, phosphorene, and anisotropic
graphene.
