periodic structure in a sentence

Examples

1. Typical choices of the groups used for voltage graphs include the two-element group $ ! 2 ( for defining the bipartite double cover of a graph ), free groups ( for defining the universal cover of a graph ), " d "-dimensional integer lattices $ ! " d " ( viewed as a group under vector addition, for defining periodic structures in " d "-dimensional Euclidean space ), and finite cyclic groups $ ! " n " for " n " > 2.