Abstract: Topology-based geometric models are important in many fields, including CAD (computer-aided design) and computer graphics. This paper introduces a general, concise, and responsive topology-based geometric data structure, called NNB-rep (nonoriented, nonmanifold boundary representation). Its generality comes from its ability to store manifold and nonmanifold geometric models, no matter whether they are degenerate or not, as needed in the first stages of the design and modeling of engineering artifacts, in particular those with cracks and degeneracies. Unlike most boundary models, the NNB-rep does not accommodate any topologically oriented cells, hence its compactness. Furthermore, despite the classical trade-off between memory and time performance, the NNB-rep is quite responsive because it hosts an optimal incidence scheme C⁹₄, which makes it adequate for a number of interactive geometric applications