A large fullerene: notice the smattering of pentagonal tiles giving rise to a spherical shape.
Having chanced upon a picture of a fullerene sphere (See above) on the internet, the question of how such structures can come about, given the providence of physics alone, suddenly dawned to me. How could a fullerene form incrementally carbon atom by carbon atom? To ultimately connect up into a sphere the carbon hexagons and pentagons have to tile in such a way as to form a sphere. Thus if we envisage an atom by atom formation of the structure it at first sight seems that the atoms need to somehow know in advance just what fullerene they are constructing so that they can arrange themselves accordingly.
So how do fullerenes form without the hands of some intelligent agent directly arranging the atoms appropriately? The only way I could think of was some kind of quantum tunneling straight through to the potential well of the structure thus allowing it to spring into sight as a fait accompli in one quantum jump. However, this is unlikely because as structures get larger the volume of the multidimensional space they occupy increases rapidly. The sought for structure then occupies such a small volume element in that space that a quantum jump to it is then highly improbable.
However, it seems that Nottingham University has come to the rescue. Using an electron microscopy technique that allows them to actually watch the formation of a fullerene, they have come up with the fullerene formation scenario. A short article on the Nottingham University Web site contains this crucial passage:
In their collaborative study the direct transformation of a graphene sheet into a perfectly formed fullerene ball has been observed for the first time - a process that for more than two decades was thought to be impossible. They observed that the fullerene ball is formed by removing carbon atoms one-by-one from the edge of the graphene sheet. Pentagons of carbon atoms can then form at the edge of the sheet allowing the graphene sheet to curve into a bowl shape. Eventually, as the graphene sheet continues to lose carbon atoms the complete fullerene ball is formed.
(See http://www.nottingham.ac.uk/Chemistry/News/FullereneformationinNature.aspx )
It looks, then, as though the "long standing puzzle" of fullerene “irreducible complexity” has or is being solved; there is, after all, an incremental path through to these structures. The providence of Physics I call that.
A Meccano Fullerene - Pity I don't have enough Meccano strips in my set to make it.