Towards a taxonomy of nets: supersymmetric 2- and 3-periodic structures in three-dimensional Euclidean space

Supersymmetric structures are defined as edge-transitive spatial graphs where the order of the site symmetry at each vertex is at least twice the coordination number of the vertex. Only 11 vertex- and edge-transitive connected periodic graphs possess this property, which we describe. We identify 32 examples of supersymmetric vertex 2-transitive, edge-transitive nets, also detailed here. Additionally, we list supersymmetric interpenetrating and interwoven structures, including weavings and polycatenanes.