Some people asked me about the pattern for making a high-genus fullerene. It is quite difficult to explain. Previously, I have posted two series pictures for creating two types of high-genus fullerenes: one consisting of octagon necks and the other for pentagon necks. They should be clear enough for anyone who try to create one.
If you want to create high-genus fullerenes in addition to these two HG-fullerenes. You have to follow more general structural rules. C. Chuang has worked out very general structural rules for constructing high-genus fullerenes belonging to tetrahedral, octahedral and icosahedral groups last year. The details have been described in this paper:
1. "Systematics of High-Genus Fullerenes." J. Chem. Inf. Model. 2009, 49, 1664-1668. DOI: 10.1021/ci9001124, ACS News & Research, July 2009.
Interestingly, this paper on the classification of High-Genus fullerenes has appeared in the "News & Research" session of ACS homepage http://portal.acs.org in July 2009.