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Similar to Weyl fermions, a recently discovered topological fermion "triplepoint" can be generated from the splitting of Dirac fermion while the systemhas inversion symmetry (IS) breaking or time reversal symmetry (TRS) breaking.Inducing triple points in IS breaking symmorphic systems have been wellstudied, whereas in TRS breaking symmorphic systems have not yet. In this work,we extend the theory of searching triple points to all symmorphic magneticsystems. We list all $k$ paths of all symmorphic systems which allow theexistence of triple points. With this systematic study, we also find out thatthe coexistence of Dirac points and triple points is symmetrically allowed insome particular symmetric systems. Our works will not only be helpful forsearching triple points but also extend the knowledge of such a new topologicalfermion.

Systematic analysis for triple points in all magnetic symmorphic systems and symmetry-allowed coexistence of Dirac points and triple points