Dechant Pierre Philippe, Wardman Jess, Keef Tom, Twarock Reidun
Mathematics Department, Durham University, Durham, DH1 3LE, England.
Mathematics Department, University of York, Heslington, York, YO10 5GG, England.
Acta Crystallogr A Found Adv. 2014 Mar;70(Pt 2):162-7. doi: 10.1107/S2053273313034220. Epub 2014 Feb 18.
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.
仿射对称原理在此应用于碳化学背景下出现的嵌套富勒烯笼(碳洋葱)。先前关于二十面体群仿射扩展的研究揭示了病毒结构和组装中的一种新组织原理。在此,这个群论框架根据碳化学的物理要求进行了调整,结果表明可以在这种仿射对称方法内推导出碳洋葱的数学模型。这表明仿射对称在自然界更广泛的背景下具有适用性,同时也为支撑碳化学的几何原理提供了一个新视角。