Reaction of a mixture of insoluble higher fullerenes with CF(3)l at 500 degrees C produced a single abundant isomer of C-74(CF3)(12), C-76(CF3)(12), and C-80(CF3)(12), two abundant isomers of C-78(CF3)(12) and C-82(CF3)(12), and an indeterminant number of isomers of C-84(CF3)(12). Using a combination of F-19 NMR spectroscopy, DFT calculations, and the structures and spectra of previously reported fullerene (CF3)(n) compounds, the most-probable structures of six of the seven isolated compounds were determined to be specific isomers of C-2-(C-74-D-3h)(CF3)(12), C-s-(C-76-T-d(2))(CF3)(12)), C-2-(C-78-D-3h(5))(CF3)(12)), C-s-(C-80-C-2v(5))(CF3)(12)), C-2-(C-82-C-2(5))-(CF3)(12)), and C-2-(C-82-C-2(3))(CF3)(12)) containing ribbons and/or loops of edge-sharing para-C-6(CF3)(2) hexagons. The seventh isolated compound is a C-1 isomer of C-78(CF3)(12) containing two such ribbons. This set of compounds represents only the second reported isolable compound with the hollow C-74-D-3h cage and the first experimental evidence for the existence of the hollow fullerenes C-76-T-d(2), C-78-D-3h(5), C-80-C-2v(5), and C-82-C-2(5) in arc-discharge soots.