We demonstrate that irregular and regular polyhedra, including Platonic and some Archimedean polyhedra, arise spontaneously in shells formed by more than one elastic component (1). Our work explains the principles to design various hallow polyhedra and the existence of regular and irregular polyhedral shells observed in some organelles, viruses and halophilic organisms. We provide experimental evidence of a new general buckling mechanism of heterogeneous shells made of mixtures of cationic and anionic molecules (2), where electrostatics drives their co-assembly, and orders the assembly into faceted ionic structures with various ionic crystalline domains (3).

1.     G. Vernizzi, R. Sknepnek, and M. Olvera de la Cruz "Platonic and Archimedean geometries in multi-component elastic membranes" Proc. Natl. Acad. Sci. USA, 118, 4292–4296 (2011).

2.     M. A. Greenfield, L. C. Palmer, G. Vernizzi, M. Olvera de la Cruz, and S. I. Stupp “Buckled Membranes in Mixed-Valence Ionic Amphiphile Vesicles”  J. Am. Chem. Soc., 131, 12030–12031 (2009).

3.     R. Sknepnek, G. Vernizzi, and M. Olvera de la Cruz “Buckling of multicomponent elastic shells with line tension” Soft Matter (DOI:10.1039/C1SM06325A ; 2011).