  This paper provides results for the spectra of triply charmed and bottom
baryons based on a constituent quark model approach. We take advantage of the
assumption that potential models are expected to describe triply heavy baryons
to a similar degree of accuracy as the successful results obtained in the
charmonium and bottomonium sectors. The high precision calculation of the
ground state and positive and negative parity excited states recently reported
by nonperturbative lattice QCD provides us with a unique opportunity to
confront model predictions with data. This comparison may also help to build a
bridge between two difficult to reconcile lattice QCD results, namely, the
lattice SU(3) QCD static three-quark potential and the recent results of
nonperturbative lattice QCD for the triply heavy-baryon spectra.
