Abstract

Membranes are abundantly present in nature. They are an essential part of most biological systems with the cell wall, the envelope of the cell nucleus, and the inner and outer mitochondrial membranes being just a few common examples. Most biological membranes are liquid and, thus, have smooth, round shapes. In other words, stress produced by the formation of a sharp edge is relieved by reordering the molecules within the membrane to round off the edge. However, there are examples of vesicles with solid membrane walls. For such membranes molecules are locked in place and there is no direct mechanism to smooth out sharp edges. As a result, the vesicles can facet. Due to an intricate interplay between geometry and elasticity, if faceted, solid vesicles take a shape of an icosahedron, or do they? In this talk, we show that a multicomponent solid shell made of two elastically distinct components can facet into a large variety of polyhedral shapes. We analyse a simple discrete model for solid membranes and explore in detail possible shape patterns of such multicomponent elastic shells with and without line tension between the two components.