Platonic and Archimedean geometries in multicomponent elastic membranes

Graziano Vernizzi, Rastko Sknepnek, Monica Olvera de la Cruz

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    59 Citations (Scopus)

    Abstract

    Large crystalline molecular shells, such as some viruses and fullerenes, buckle spontaneously into icosahedra. Meanwhile multicomponent microscopic shells buckle into various polyhedra, as observed in many organelles. Although elastic theory explains one-component icosahedral faceting, the possibility of buckling into other polyhedra has not been explored. We show here that irregular and regular polyhedra, including some Archimedean and Platonic polyhedra, arise spontaneously in elastic shells formed by more than one component. By formulating a generalized elastic model for inhomogeneous shells, we demonstrate that coassembled shells with two elastic components buckle into polyhedra such as dodecahedra, octahedra, tetrahedra, and hosohedra shells via a mechanism that explains many observations, predicts a new family of polyhedral shells, and provides the principles for designing microcontainers with specific shapes and symmetries for numerous applications in materials and life sciences.

    Original languageEnglish
    Pages (from-to)4292-4296
    Number of pages5
    JournalProceedings of the National Academy of Sciences of the United States of America
    Volume108
    Issue number11
    DOIs
    Publication statusPublished - 15 Mar 2011

    Keywords

    • self-assembly
    • crystalline shells
    • SYMMETRY
    • PRINCIPLES
    • BACTERIAL MICROCOMPARTMENTS
    • SHAPE
    • PROTEINS
    • CARBOXYSOMES
    • DEFECTS
    • DYNAMICS
    • VIRUSES

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