Yong, Ee HouNelson, DavidMahadevan, Lakshminarayanan2014-12-032013Yong, Ee Hou, David R. Nelson, and Lakshminarayanan Mahadevan. 2013. "Elastic Platonic Shells." Physical Review Letters 111 (17): 177801.0031-90071079-7114http://nrs.harvard.edu/urn-3:HUL.InstRepos:13457748On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading or unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.en-USJournal Article2014-12-0310.1103/PhysRevLett.111.177801