Lenticular Hexagon-to-Hexagram Shape Transformation: Nano-Origami in Liquid Droplets

Temperature-controlled droplet shape transformations have been extensively studied, uncovering the mechanism of convex liquid polyhedron formation but failing to account for concave edges. Here, we reveal interfacially frozen metastable droplets with hexagram projections and concave edges. We combine macroscopic experiments, numerical simulations, and an analytical geometric model, elucidating the mechanism of these phenomena: previously unreported, mobile-fold nano-origami. Our findings open new avenues in self-assembly of complex faceted liquid and solid nanostructures for nanotechnology applications.