We report high-resolution far-infrared transmission measurements of the 2 + 2 cycloaddition C-60 dimer and two-dimensional rhombohedral and one-dimensional orthorhombic high-pressure high-temperature C60 polymers. In the spectral region investigated(20-650 cm(-1)), we see no low-energy interball modes, but symmetry breaking of the linked C-60 balls is evident in the complex spectrum of intramolecular modes. Experimental features suggest large splittings or frequency shifts of some IhC60-derived modes that are activated by symmetry reduction, implying that the balls are strongly distorted in these structures. We have calculated the vibrations of all three systems by first-principles quantum molecular dynamics and use them to assign the predominant IhC60 symmetries of observed modes. Pur calculations show unprecedentedly large downshifts of T-1u(2)-derived modes and extremely large splittings of other modes, both of which are consistent with the experimental spectra. For the rhombohedral and orthorhombic polymers, the T-1u(2)-derived mode that is polarized along the bonding direction is calculated to downshift below any T-1u(1)-derived modes. We also identify a previously unassigned feature near 610 cm(-1) in all three systems as a widely split or shifted mode derived from various silent IhC60 vibrations, confirming a strong perturbation model for these linked fullerene structures.