  Topological phases can not only be protected by internal symmetries (e.g.,
time-reversal symmetry), but also by crystalline symmetries, such as reflection
or rotation symmetry. Recently a complete topological classification of
reflection symmetric insulators, superconductors, nodal semimetals, and nodal
superconductors has been established. In this article, after a brief review of
the classification of reflection-symmetry-protected semimetals and nodal
superconductors, we discuss an example of a three-dimensional topological Dirac
semimetal, which exhibits time-reversal symmetry as well as reflection and
rotation symmetries. We compute the surface state spectrum of this Dirac
semimetal and identify the crystal lattice symmetries that lead to the
protection of the surface states. We discuss the implications of our findings
for the stability of the Fermi arc surface states of the Dirac material
Na$_3$Bi. Our analysis suggests that the Fermi arc of Na$_3$Bi is gapped except
at time-reversal invariant surface momenta, which is in agreement with recent
photoemission measurements.
