C-60(+) ions were produced by electron-impact ionization of sublimed C-60, collimated into an ion beam, turned 90 degrees by an electrostatic deflector to separate them from neutrals, mass filtered by a radio frequency quadrupole, and co-deposited with Ne on a cold 5 K gold-coated sapphire substrate. Infrared absorption spectroscopy revealed the additional presence of C-60 and C-60(-) in the as-prepared cryogenic matrixes. To change the C-60(+)/C-60(-) ratio, CCl4 or CO2 electron scavengers were added to the matrix gas. Also taking into account DFT calculations, we have identified nine new previously unpublished IR absorptions of C-60(+) and seven of C-60(-) in Ne matrixes. Our measurements are in very good agreement with DFT calculations, predicting D-5d C-60(+) and D-3d C-60(-) ground states. The new results may be of interest regarding the presence of C-60 and C-70 (as well as ions thereof) in Space.