Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain
the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in
Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles
and JavaScript.
Group theory is a formal method for analysing, in terms of symmetry groups, abstract and physical systems in which symmetry is present. For example, group theory classifies regular polyhedra, crystal structures and the symmetries of molecules.
Models for polyhedral clusters with different symmetries enable us to understand their electronic structures and predict the formation of new clusters.