  In iron-based superconductors, band inversion of $d$- and $p$-orbitals yields
Dirac semimetallic states. We theoretically investigate their topological
properties in normal and superconducting phases, based on the tight-binding
model involving full symmetry of the materials. We demonstrate that a Cooper
pair between electrons with $d$- and $p$-orbitals relevant to the band
structure yields odd-parity superconductivity. Moreover, we present the typical
surface states by solving the Bogoliubov-de Gennes equation and characterize
them by topological invariants defined with crystal symmetry. It is found that
there appear various types of Majorana fermions such as surface flat band,
Majorana quartet and M\"{o}bius twisted surface state. Our theoretical results
show that iron-based superconductors are promising platforms to realize rich
topological crystalline phases.
