  We apply here the principle of affine symmetry to the nested fullerene cages
(carbon onions) that arise in the context of carbon chemistry. Previous work on
affine extensions of the icosahedral group has revealed a new organisational
principle in virus structure and assembly. We adapt this group theoretic
framework here to the physical requirements dictated by carbon chemistry, and
show that we can derive mathematical models for carbon onions within this
affine symmetry approach. This suggests the applicability of affine symmetry in
a wider context in Nature, as well as offering a novel perspective on the
geometric principles underpinning carbon chemistry.
