FOLLOWING the development of a method for bulk synthesis of C60 and other fullerenes1, the isolation of higher fullerenes ranging from C76 to C96 has been achieved using chromatographic techniques2–5. Whereas C60 and C70 have unique, high-symmetry structures6, theoretical calculations for fullerenes larger than C76 have suggested that each may exist in at least two isomeric forms7. For C84, 24 isomers have been postulated7, and for C96calculations have yielded 196 distinct isomers8. Diederich et al.9 have used liquid chromatography and 13C NMR to identify two isomers of C78, but previous experimental studies of other higher fullerenes2 have produced ambiguous results. Here we use 13C NMR to determine the structures of some principal isomers of C78, C82 and C84. We find a third isomer of C78, which was not reported in ref. 9. Characterization of the structures of these larger fullerenes should provide new understanding of the factors determining the stability of hollow carbon clusters.