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Shape-changing objects are prized for applications ranging from acoustics to robotics. We report sub-millimetre bubbles that reversibly and rapidly change not only their shape but also their topological class, from sphere to torus, when subjected to a simple pressure treatment. Stabilized by a solid-like film of nanoscopic protein “particles”, the bubbles may persist in toroidal form for several days, most of them with the relative dimensions expected of Clifford tori. The ability to cross topological classes reversibly and quickly is enabled by the expulsion of protein from the strained surfaces in the form of submicron assemblies. Compared to structural modifications of liquid-filled vesicles, for example by slow changes in solution osmolality, the rapid inducement of shape changes in bubbles by application of pressure may hasten experimental investigations of surface mechanics, even as it suggests new routes to lightweight materials with high surface areas.