Kavli Affiliate: Mark Bowick
| First 5 Authors: Mark Bowick, Rastko Sknepnek, , ,
| Summary:
The interplay between geometry, topology and order can lead to geometric
frustration that profoundly affects the shape and structure of a curved
surface. In this commentary we show how frustration in this context can result
in the faceting of elastic vesicles. We show that, under the right conditions,
an assortment of regular and irregular polyhedral structures may be the low
energy states of elastic membranes with spherical topology. In particular, we
show 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 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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