This short article consists of some thoughts derived from a longer paper (Palmer, 1992), together with some more recent ideas. I became interested in buckminsterfullerene (Buckyballs) as a result of an E-Mail discussion of the topic in 1991. The chemistry of buckyballs is now evolving very rapidly and is gradually creeping into school curricula. The focus of this article is thus not on buckminsterfullerene, but on how, at what level and in what form, material about buckyballs is being or should be included in school curricula.