The structure and stability of a set of (CF)(60) isomers have been computed at the B3LYP/6-31 G(d) density functional theory level. The most stable isomer (6, F-4@C-60)F-56) has tube-like structure with four endo C-F bonds and fused five-membered rings at the end of the tube, while the reported most stable cage structure (2, F-8@C60F52) with eight endo C-F bonds is higher in energy by 22.6 kcal/mol. This is in contrast to the isolated pentagon rule for the stability of fullerenes. The mean bond dissociation energy of 6 is larger than those of the experimental known C60F36, C60F48, and graphite fluoride. The relative energy per CF unit of 6 to graphite fluoride (CF)(n) is 3.7 kcal/mol, which is smaller than that of C-60 fullerene per carbon to graphite (about 9-10 kcal/mol).