  Triply heavy baryons are very interesting systems analogous to heavy
quarkonia, but are difficult to access experimentally. Lattice QCD can provide
precise predictions for these systems, which can be compared to other
theoretical approaches. In this work, the spectrum of excited states of the
Omega_bbb baryon is calculated using lattice NRQCD for the b quarks, and using
a domain-wall action for the u, d and s sea quarks. The calculations are done
for multiple values of the sea-quark masses, and for two different lattice
spacings. The energies of states with angular momentum up to J=7/2 are
calculated, and the effects of rotational symmetry breaking by the lattice are
analyzed. Precise results are obtained even for the small spin-dependent energy
splittings, and the contributions of individual NRQCD interactions to these
energy splittings are studied. The results are compared to potential-model
calculations.
