Number of extractable fullerene isomers and speciality of C84

We study the topology of all pentagon isolated fullerenes from C60 to C90 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 C84 is much larger than that for other fullerenes. This corresponds not only to the extraction of a larger amount of C84 than other fullerenes but also to the existence of more than three isomers for C84 revealed from recent experiments.