  Baryons with three heavy quarks are the last missing pieces of the
lowest-lying baryon multiplets in the quark model after the discovery of doubly
heavy baryons. In this work, we study nonleptonic weak decays of triply heavy
baryons $\Omega_{ccc}^{++}$, $\Omega_{bbb}^{-}$, $\Omega_{ccb}^{+}$, and
$\Omega_{cbb}^{0}$. Decay amplitudes for various processes have been
parametrized in terms of the SU(3) irreducible nonperturbative amplitudes. A
number of relations for the partial decay widths can be deduced from these
results that can be examined in future. Some decay channels and cascade decay
modes which likely to be used to reconstruct the triply heavy baryons have been
also listed.
