Storing a 3d City Model, its Levels of Detail and the Correspondences Between Objects as a 4d Combinatorial Map

3D city models of the same region at multiple LODs are encumbered by the lack of links between corresponding objects across LODs. In practice, this causes inconsistency during updates and maintenance problems. A radical solution to this problem is to model the LOD of a model as a dimension in the geometric sense, such that a set of connected polyhedra at a series of LODs is modelled as a single polychoron—the 4D analogue of a polyhedron. This approach is generally used only conceptually and then discarded at the implementation stage, losing many of its potential advantages in the process. This paper therefore shows that this approach can be instead directly realised using 4D combinatorial maps, making it possible to store all topological relationships between objects.