title: Viruses and fullerenes--symmetry as a common thread?
abstract: The principle of affine symmetry is applied here 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 organizational principle in virus structure and assembly. This group-theoretic framework is adapted here to the physical requirements dictated by carbon chemistry, and it is shown that mathematical models for carbon onions can be derived 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.
authors.affiliation: Mathematics Department, Durham University, Durham, DH1 3LE, England.
authors.forename: Pierre Philippe
authors.initials: PP
authors.lastname: Dechant
authors.affiliation: Mathematics Department, University of York, Heslington, York, YO10 5GG, England.
authors.forename: Jess
authors.initials: J
authors.lastname: Wardman
authors.affiliation: Mathematics Department, University of York, Heslington, York, YO10 5GG, England.
authors.forename: Tom
authors.initials: T
authors.lastname: Keef
authors.affiliation: Mathematics Department, University of York, Heslington, York, YO10 5GG, England.
authors.forename: Reidun
authors.initials: R
authors.lastname: Twarock
mesh_terms: D002244:Carbon / Q000737:chemistry*; D003460:Crystallization; D037741:Fullerenes / Q000737:chemistry*; D008958:Models, Molecular; D014780:Viruses / Q000737:chemistry*
chemical_list: D037741:Fullerenes; D002244:Carbon
keywords: Coxeter groups; affine extensions; carbon onions; fullerenes; quasicrystals; symmetry; viruses