Systems and methods are provided for connecting flat sheets formed from a variety of different materials to construct three-dimensional self-supporting structures having predetermined shapes and decorative and/or functional purposes. The flat sheets, which also may be referred to as individual components, may each include a plurality of prong sets and a plurality of slits whereby a prong set from an individual component may be inserted into a slit of another individual component to interlock and form a joint between the individual components. Each individual component may form one or more joints with the other individual components. The tension created in the joints may provide depth to the surface, which in turn may create structure.