Whilst new patents and announcements advertise the technical availability of foldable displays, which are capable to be folded to some extent, there is still a lack of fundamental and applied understanding of how to model, to design, and to prototype graphical user interfaces for these devices before actually implementing them. Without waiting for their off-the-shelf availability and without being tied to any physical foldable mechanism,Flecto defines a model, an associated notation, and a supporting software for prototyping graphical user interfaces running on foldable displays, such as foldable smartphone or assemblies of foldable surfaces. For this purpose,the Yoshizawa-Randlett diagramming system, used to describe the folds of origami models, is extended to characterize a foldable display and define possible interactive actions based on its folding operations. A guiding method for rapidly prototyping foldable user interfaces is devised and supported by Flecto, a design environment where foldable user interfaces are simulated in virtual reality instead of in physical reality. We report on a case study to demonstrate Flecto in action and we gather the feedback from users on Flecto, using Microsoft Product Reaction Cards.