  It is shown that the Wilson fermion doubling phenomenon on irregular lattices
(simplicial complexes) does exist. This means that the irregular (not smooth)
zero or soft modes exist. The statement is proved on 4 Dimensional lattice by
means of the Atiyah-Singer index theorem, then it is extended easily into the
cases $D<4$. But there is a fundamental difference between doubled quanta on
regular and irregular lattices: in the latter case the propagator decreases
exponentially. This means that the doubled quanta on irregular lattice are
"bad" quasiparticles.
