LAUSR

Significance Three-dimensional shaping of thin sheets and membranes is a ubiquitous feature of materials science and underlies diverse biological processes, ranging from large-scale morphogenesis to molecular drug delivery. It is also a familiar everyday phenomenon, as illustrated by the formation of soap bubbles. We demonstrate how flat disk–shaped colloidal membranes transform into saddle-like surfaces. As membranes coalesce, the saddle-shaped surfaces form catenoid-like structures and other architectures of increasing complexity and topological genus. The unique features of our experiments reveal the three-dimensional details of the pathway by which membranes undergo topological shape changes in real time. Our results demonstrate the topological shaping of membrane-like materials through control of their elasticity and Gaussian curvature modulus.