Meshing is an important topic in geometric modelling and computer graphics. This paper introduces a concise and fast data structure, called AIF (Adjacency and Incidence Framework). Its conciseness results from the fact that it is an orientable, but not an oriented, data structure, i.e. an orientation can be topologically induced as necessary in many applications. It is an optimal C ₉ ⁴ data structure for polygonal meshes, manifold and non-manifold, which means that a minimal number of direct and indirect accesses are required to retrieve adjacency and incidence information from it. In fact, it operates close to real-time even for huge meshes, what becomes it appropriate for real-time applications (e.g. multiresolution meshing refinement and simplification operations).