Number of extractable fullerene isomers and speciality of C-84

We study the topology of all pentagon isolated fullerenes from C-60 to C-90 with respect to pentagon arrangements and residual component units. Since 12 pentagons can be grouped into 6 pairs and an even number of atom chains is preferred in extractable fullerenes, we can considerably reduce the number of candidates for extractable large fullerenes. From this study, we report the number of preferable isomers for each size of fullerenes. We have found that the number of preferable isomers for C-84 is much larger than that for other fullerenes. This corresponds not only to the extraction of a larger amount of C-84 than other fullerenes but also to the existence of more than three isomers for C-84 revealed from recent experiments.