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Every soccer ball has 12 pentagons, even when it is deflated. In his Perspective, Kamien describes how Bausch et al. exploit this topological property in the design of complex new materials based on the self-assembly of two-dimensional colloidal crystals on spheres. The work is an example of a growing trend in materials science to control not only the geometry but also the connectivity (and hence topology) of molecules in self-assembled materials. The approach reported by Bausch et al. is particularly powerful because it is not dependent on specific interactions and should therefore allow the assembly of a wide range of hierarchical, self-assembled materials.