Coordination framework polymers derived from lanthanide metal ions with N,N ‘-dioxide ligands (4,4‘-bipyridine-N,N‘-dioxide, pyrazine-N,N‘-dioxide, 1,2-bis(pyridin-4-yl)ethane-N,N‘-dioxide, trans-1,2-bis(pyridin-4-yl)ethene-N,N‘-dioxide) exhibit such intricate architectures that a new strategy is required to appreciate and understand their structures. Rather than analyzing the overall structure in terms of the connectivity of individual metal nodes, which can lead in some cases to extremely complex topological treatments, our new strategy is based on the visualization of the structures as combinations of interconnected layered 2-D sheets or subnet tectons. Despite the diversity and relative complexities of many of the structures discussed here, they can all be described by the interconnection of just two types of 2-D subnet tectons, 44 square grids or 63 hexagonal grids. The interconnection of these layered sheets with bridging N,N ‘-dioxide molecules gives rise to both 2-D bilayer and 3-D network extended structures depending upon the relative dispositions of the interconnecting N,N ‘-dioxide ligands. Thus, 2-D bilayers result when the N,N ‘-dioxide ligands that bridge two subnet tectons are located on the same side of the sheet, while 3-D networks are formed when the bridging N,N ‘-dioxide ligands are located on both sides of the sheet. This analysis allows ready identification and interpretation of some of the most highly connected and complex architectures yet observed in materials chemistry.