Pathways to faceting of vesicles

TL;DR

This paper explores how geometric frustration in elastic vesicles can lead to faceted structures, including polyhedra like icosahedra, influenced by topological defects and elastic heterogeneities.

Contribution

It demonstrates how frustration causes vesicles to adopt faceted shapes, revealing pathways to non-icosahedral structures through heterogeneities and non-linear responses.

Findings

Topological defects induce icosahedral faceting in vesicles.

Heterogeneities enable formation of non-icosahedral faceted structures.

Non-linear bending responses open new pathways to vesicle faceting.

Abstract

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.