The structures of higher fullerenes are described based on 13C NMR measurements of isolated and purified samples. The most interesting aspect deduced from the present structural work on the higher fullerenes up to C90 is that among 19 kinds of fullerenes with different sizes and isomers, 18 fullerenes commonly have at least one C2 symmetry axis in their molecular frame. Only one exception is C90 fullerene with a C1 symmetry. The spectral feature of UV/Visible absorption obtained for the HPLC-isolated C120 fullerene gives, on the other hand, a strong indication that the numbers of co-existing isomer of very large fullerenes are extremely limited, probably one or two. Considering the huge numbers of IPR-(isolated pentagon rule) satisfying isomer of C120 (10,774), these experimental evidences may suggest the presence of very strong selectivity for the formation of stable higher fullerenes, which, in turn, is closely associated with the unknown growth process of a fullerene cage network.