Much of recent research in representation schemes for solid modeling was focused on the extension of boundary representations to support non-manifold topologies. We introduce here a very simple, yet general formalism, which subsumes and simplifies many previous attempts at defining high-level operators for creating and interrogating such models. Our Structured Topological Complex (STC) extends our previous work on Selective Geometric Complexes (SGC) and on Constructive Non-Regularized Geometry (CNRG) and provides the foundations for a new generation of representations−both constructive and evaluated−and of APIs that are independent of the particular geometric domain and even of the particular approximation scheme for geometric primitives.