We determine the phase diagram of the O(n) loop model on the honeycomb lattice, in particular, in therange n＞2, by means of a transfer-matrix method. We find that, contrary to the prevailing expectation,there is a line of critical points in the range between n＝2 and ∞. This phase transition, which belongsto the three-state Potts universality class, is unphysical in terms of the O (n) spin model, but falls insidethe physical region of the n-component corner-cubic model. It can also be interpreted in terms of theordering of a system of soft particles with hexagonal symmetry.