Adding 1% of the metallic elements cerium, lanthanum, and yttrium to graphite rod electrodes resulted in different amounts of the hollow higher fullerenes (HHFs) C-76-D-2(1), C-78-C-2v(2), and C-78-C-2v(3) in carbon-arc fullerene-containing soots. The reaction of trifluoroiodomethane with these and other soluble HHFs at 520-550 degrees C produced 21 new C-76,C-78,C-84,C-90(CF3)(n) derivatives (n = 6, 8, 10, 12, 14). The reaction with C-76-D-2(1) produced an abundant isomer of C-2-(C-76-D-2(1))(CF3)(10) plus smaller amounts of an isomer of C-1-(C-76-D-2(1))(CF3)(6), two isomers of C-1-(C-76-D-2(1))(CF3)(8), four isomers of C-1-(C-76-D-2(1))(CF3)(10), and one isomer of C-2-(C-76-D-2(1))(CF3)(12). The reaction with a mixture of C-78-D-3(1), C-78-C-2v(2), and C-78-C-2v(3) produced the previously reported isomer C-1-(C-78-C-2v(3))(CF3)(12) (characterized by X-ray crystallography in this work) and the following new compounds: C-2-(C-78-C-2v(3))(CF3)(8); C-2-(C-78-D-3(1))(CF3)(10) and C-s-(C78-C-2v(2))(CF3)(10) (both characterized by X-ray crystallography in this work); C-2-(C-78-C-2v(2))(CF3)(10); and C-1-C-78(CF3)(14) (cage isomer unknown). The reaction of a mixture of soluble higher fullerenes including C-84 and C-90 produced the new compounds C-1-C-84(CF3)(10) (cage isomer unknown), C-1-(C-84-C-2(11))(CF3)(12) (X-ray structure reported recently), D-2-(C-84-D-2(22))(CF3)(12), C-2-(C-84-D-2(22))(CF3)(12), C-1-C-84(CF3)(14) (cage isomer unknown), C-1-(C-90-C-1(32))(CF3)(12), and another isomer of C-1-C-90(CF3)(12) (cage isomer unknown). All Compounds were studied by mass spectrometry, F-19 NMR spectroscopy, and DFT calculations. An analysis of the, addition patterns of these compounds and three other HHF(X)(n) compounds with bulky X groups has led to the discovery of the following addition-pattern principle for HHFs: In general, the most pyramidal cage C(sp(2)) atoms in the parent HHF, which form the most electron-rich and therefore the most reactive cage C-C bonds as far as 1,2-additions are concerned, are not the cage C atoms to which bulky substituents aria added. Instead, ribbons of edge-sharing P-C-6(X)(2) hexagons, with X groups on less pyramidal cage C atoms, are formed, and the otherwise "most reactive" fullerene double bonds remain intact.