Construction of higher fullerenes belonging either to I or Ih point groups is an interesting experience to me. There are not many of them, compared with all possible isomers. It seems to me it is not necessary to use the spiral algorithm I describe before. The symmetry of the systems pose a strong limitation on the possible positions of pentagons. By inspection, we can find out the systematic strategy for generating all possible higher fullerenes. I will explain my strategy later. Here are all possible I or Ih fullerene with the number of carbon atoms less 300.
C60(Ih), C80(Ih), C140(I), C180(Ih), C240(Ih), C260(I)
Honestly speaking, the colors I chose for these compounds are terrible. I am thinking about remaking these models. Maybe some of you can help.