Four-wave mixing measurements are carried out on I(2)-doped ice, prepared by quench condensing the premixed vapor at 128 K. Coherent vibrational dynamics is observed in two distinct ensembles. The first is ascribed to trapping in asymmetric polar cages in which, as in water, the valence absorption of the molecule is blueshifted by 3500 cm(-1), predissociation of the B state is complete upon the first extension of the molecular bond, and the vibrational frequency in the ground state (observed through coherent anti-Stokes Raman scattering) is reduced by 6.5%. The effect is ascribed to polarization of the molecule. The implied local field and the ionicity of the molecule are extracted, to conclude that the molecule is oxygen bonded to one water molecule on one side and hydrogen bonded on the other side. The second ensemble is characterized by the transient grating signal, which shows coherent vibrational dynamics on the B state. The small predissociation rate in this site suggests a symmetric cage in which the local electric field undergoes effective cancellation; and consistent with this, the extracted blueshift of the valence transition in this site (approximately 1500 cm(-1)) coincides with that observed in clathrate hydrates of iodine. Remarkably, in this site, the vibrational period of the B state packet coherently stretches from an initial value of 245 fs to 325 fs in the course of five oscillations (1.3 ps), indicative of vibrationally adiabatic following of the cage expansion. The dynamics is characteristic of a molecule trapped in a tight symmetric cage, with a soft cage coordinate that relaxes without eliciting elastic response. Enclathration in low-density amorphous ice is concluded.