Mechanical duality in Maxwell and non-Maxwell lattices

Duality is an important concept, which plays a crucial role in a wide range of physics problems. Recently, it is shown that in mechanical systems, duality can give rise to highly nontrivial phenomena, such as non-Abelian mechanics. In this talk, we study mechanical duality in Maxwell and non-Maxwell lattices as well as its connection to emergent higher symmetries, topological indices and topological edge states. Based on the graph connectivity of the underlaying lattice structure, we show that systems with mechanical duality can be classified in two classes. We identify universal elastic properties for each class and demonstrate this physics in various model systems. In addition, from these studies, we observed rich and unexpected phenomena, such as flat bands, self-dual lines and self-dual manifold.