  $k$ paths exactly with $C_{3v}$ symmetry allow to find triply degenerate
points (TDPs) in band structures. The paths that host the type-II Dirac points
in PtSe$_2$ family materials also have the $C_{3v}$ spatial symmetry. However,
due to Kramers degeneracy (the systems have both inversion symmetry and time
reversal symmetry), the crossing points in them are Dirac ones. In this work,
based on symmetry analysis, first-principles calculations, and $k\cdot p$
method, we predict that PtSe$_2$ family materials should undergo topological
transitions if the inversion symmetry is broken, \emph{i.e.} the Dirac fermions
in PtSe$_2$ family materials split into TDPs in PtSeTe family materials (PtSSe,
PtSeTe, and PdSeTe) with orderly arranged S/Se (Se/Te). It is different from
the case in high-energy physics that breaking inversion symmetry $I$ leads to
the splitting of Dirac fermion into Weyl fermions. We also address a possible
method to achieve the orderly arranged in PtSeTe family materials in
experiments. Our study provides a real example that Dirac points transform into
TDPs, and is helpful to investigate the topological transition between Dirac
fermions and TDP fermions.
