The spectrum of excitations of triply-charmed baryons is computed using lattice QCD including dynamical light quark fields. Calculations are performed on anisotropic lattices with temporal and spatial spacings a_t = 0.0351(2) and a_s ~ 0.12 fm respectively and with pion mass of about 390 MeV. The spectrum obtained has baryonic states with well-defined total spin up to 7/2 and the low-lying states closely resemble the expectation from models with an SU(6)X O(3) symmetry. Energy splittings between extracted states, including those due to spin-orbit coupling in the heavy quark limit are computed and compared against data at other quark masses.
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