Platonic and Archimedean geometries in multicomponent elastic membranes

Graziano Vernizzi, Rastko Sknepnek, Monica Olvera de la Cruz

    Research output: Contribution to journalArticle

    53 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

    Cite this

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    title = "Platonic and Archimedean geometries in multicomponent elastic membranes",
    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.",
    keywords = "self-assembly, crystalline shells, SYMMETRY, PRINCIPLES, BACTERIAL MICROCOMPARTMENTS, SHAPE, PROTEINS, CARBOXYSOMES, DEFECTS, DYNAMICS, VIRUSES",
    author = "Graziano Vernizzi and Rastko Sknepnek and {de la Cruz}, {Monica Olvera}",
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    doi = "10.1073/pnas.1012872108",
    language = "English",
    volume = "108",
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    journal = "Proceedings of the National Academy of Sciences",
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    Platonic and Archimedean geometries in multicomponent elastic membranes. / Vernizzi, Graziano; Sknepnek, Rastko; de la Cruz, Monica Olvera.

    In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 108, No. 11, 15.03.2011, p. 4292-4296.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Platonic and Archimedean geometries in multicomponent elastic membranes

    AU - Vernizzi, Graziano

    AU - Sknepnek, Rastko

    AU - de la Cruz, Monica Olvera

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    Y1 - 2011/3/15

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    AB - 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.

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    KW - BACTERIAL MICROCOMPARTMENTS

    KW - SHAPE

    KW - PROTEINS

    KW - CARBOXYSOMES

    KW - DEFECTS

    KW - DYNAMICS

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