We use two-body potentials derived from a constituent quark cluster model to analyze the bound-state problem of the ΣN N system. The observables of the two-body subsystems, N N and ΣN , are well reproduced. We do not find ΣN N bound states, but there are two attractive channels with a resonance close above the three-body threshold. These channels are the (I, J) = (1, 1/2) and (0, 1/2), their quantum numbers, widths and energy ordering consistent with the recently measured strange tribaryons from the 4 He(K