New generation thin, lightweight and damage-resistant glass seems to be the optimal material for extremely deformable structural elements for façades and building skins. Here, an innovative concept is proposed, based on the use of cold-twisted square elements and on the exploitation of their buckling phenomenon, causing the shape modification from double-curvature anticlastic to single-curvature shape, where bending essentially occurs along one diagonal. This is applied to the design of a transformable greenhouse for protected agriculture, suitable for strong modification of openings and ventilation, allowing to fully exploit the high-deformability of thin glass. The greenhouse roof is composed by four curved thin glass elements, with a metallic frame designed to provide a preferential direction for the bending deformation, having the semblance of “petals”. The cell’s curvature can be modified by changing the support’s position. This allows to modify not only the shape and the inclination of the surfaces forming the roof, thus changing lighting and irradiation, but also size and shape of the openings, strongly affecting the air flow. Numerical analyses and “design-by-prototyping” strategy, entailing the construction of a reduced-scale mock-up of the greenhouse, have demonstrated the feasibility of this concept, highlighting the huge range of obtainable configurations and opening systems.