A. D. Alexandrov proved a remarkable theorem that gives a necessary and sufficient condition for a simple polygonal figure on a plane to be folded into a convex polyhedron by glueing its edges. In some cases, a single figure admits multiple ways to glue its boundary to yield different convex polyhedra. A few algorithms have been developed to enumerate glueing patterns on a fixed polygonal figure that satisfy Alexandrov’s condition. Based on these facts, we introduce a physical puzzle consisting of hinged panels that can be folded into different polyhedra. The puzzle challenges one’s three-dimensional perception with a tangible object.