Adding 1% of the metallic elements cerium, lanthanum, and yttrium to graphite rod electrodes resulted in different amounts of the hollow higher fullerenes (HHFs) C76-D2(1), C78-C2v(2), and C78-C2v(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 C76,78,84,90(CF3)n derivatives (n = 6, 8, 10, 12, 14). The reaction with C76-D2(1) produced an abundant isomer of C2-(C76-D2(1))(CF3)10 plus smaller amounts of an isomer of C1-(C76-D2(1))(CF3)6, two isomers of C1-(C76-D2(1))(CF3)8, four isomers of C1-(C76-D2(1))(CF3)10, and one isomer of C2-(C76-D2(1))(CF3)12. The reaction with a mixture of C78-D3(1), C78-C2v(2), and C78-C2v(3) produced the previously reported isomer C1-(C78-C2v(3))(CF3)12 (characterized by X-ray crystallography in this work) and the following new compounds: C2-(C78-C2v(3))(CF3)8; C2-(C78-D3(1))(CF3)10 and C(s)-(C78-C2v(2))(CF3)10 (both characterized by X-ray crystallography in this work); C2-(C78-C2v(2))(CF3)10; and C1-C78(CF3)14 (cage isomer unknown). The reaction of a mixture of soluble higher fullerenes including C84 and C90 produced the new compounds C1-C84(CF3)10 (cage isomer unknown), C1-(C84-C2(11))(CF3)12 (X-ray structure reported recently), D2-(C84-D2(22))(CF3)12, C2-(C84-D2(22))(CF3)12, C1-C84(CF3)14 (cage isomer unknown), C1-(C90-C1(32))(CF3)12, and another isomer of C1-C90(CF3)12 (cage isomer unknown). All compounds were studied by mass spectrometry, (19)F 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 are added. Instead, ribbons of edge-sharing p-C6(X)2 hexagons, with X groups on less pyramidal cage C atoms, are formed, and the otherwise "most reactive" fullerene double bonds remain intact.