Nature of the equivalence between gamma instability and rigid triaxiality for finite boson number

Recently, it was observed that the O(6) limit of the interacting boson model for moderate boson number was equivalent to both a γ unstable rotor and a rigid triaxial rotor with γ = 300. Here it is shown that the proof given for this equivalence does not show that the eigenstates are equivalent in the two pictures but only that the subspaces for the low lying states are equivalent. A plausibility argument based on a dynamical symmetry of the γ = 300 rigid rotor is given which suggests that the excited states of the O(6) system are not equivalent to the excited states of the rigid triaxial rotor. The ground states, however, are equivalent