Mark Bowick, Rastko Sknepnek
An interplay between geometry, topology, and order can lead to geometric frustration that profoundly affects the shape and structure of a curved surface. In this paper we discuss how such effects can result in faceting of elastic vesicles. We show that under the right conditions an assortment of regular and irregular polyhedral structures can be the low energy states of such elastic objects. In particular, we discuss how topological defects necessarily present in any crystalline lattice confined to spherical topology naturally lead to the formation of icosahedra in a homogeneous elastic vesicle. Furthermore, we show that introducing heterogeneities in the elastic properties or allowing for a non-linear bending response of a homogeneous system opens non-trivial pathways to the formation of faceted, yet non-icosahedral structures.
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http://arxiv.org/abs/1303.1793
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