  Gapless topological phases of matter may host emergent quasiparticle
excitations which have no analog in quantum field theory. This is the case of
so called triple point fermions (TPF), quasiparticle excitations protected by
crystal symmetries, which show fermionic statistics but have an integer
(pseudo)spin degree of freedom. TPFs have been predicted in certain
three-dimensional non-symmorphic crystals, where they are pinned to high
symmetry points of the Brillouin zone. In this work, we introduce a minimal,
three-band model which hosts TPFs protected only by the combination of a C4
rotation and an anti-commuting mirror symmetry. Unlike current non-symmorphic
realizations, our model allows for TPFs which are anisotropic and can be
created or annihilated pairwise. It provides a simple, numerically affordable
platform for their study.
