Shape-changing polyhedra are defined as three-dimensional polygonal and modular structures that interconnect and change shape and size. Applications include art, architecture, and engineering. Shape-changing polyhedra are composed of flexibly connected polygons. In their modular forms they can interconnect, one with another, such that when one shape-changes then all shape-change. Shape-changing polyhedra can be macro, micro, or nano sized. There may be thousands of interesting shape-changing polyhedra to discover.