  Degeneracy (exceptional) points embedded in energy band are distinct by their
topological features. We report different hybrid two-state coalescences (EP2s)
formed through merging two EP2s with opposite chiralities that created from the
type III Dirac points emerging from a flat band. The band touching hybrid EP2,
which is isolated, is induced by the destructive interference at the proper
match between non-Hermiticity and synthetic magnetic flux. The degeneracy
points and different types of exceptional points are distinguishable by their
topological features of global geometric phase associated with the scaling
exponent of phase rigidity. Our findings not only pave the way of merging EPs
but also shed light on the future investigations of non-Hermitian topological
phases.
