Platonic and Archimedean geometries in multicomponent elastic membranes

Graziano Vernizzi, Rastko Sknepnek, Monica Olvera De La Cruz

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


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 (US)
Pages (from-to)4292-4296
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number11
StatePublished - Mar 15 2011


  • Crystalline shells
  • Self-assembly

ASJC Scopus subject areas

  • General

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