While CityGML permits us to represent 3D city models, its use for applications where spatial analysis and/or real-time modifications are required is limited since at this moment the possibility to store topological relationships between the elements is rather limited and often not exploited. We present in this paper a new topological data structure, the dual half-edge (DHE), which permits us to represent the topology of 3D buildings (including their interiors) and of the surrounding terrain. It is based on the idea of simultaneously storing a graph in 3D space and its dual graph, and to link the two. We propose Euler-type operators for incrementally constructing 3D models (for adding individual edges, faces and volumes to the model while updating the dual structure simultaneously), and we also propose navigation operators to move from a given point to all the connected planes or polyhedra for example. The DHE also permits us to store attributes to any element. We have implemented the DHE and have tested it with different CityGML models. Our technique allows us to handle important query types, for example finding the nearest exterior exit to a given room, as in disaster management planning. As the structure is locally modifiable the model may be adapted whenever a particular pathway is no longer available. The proposed DHE structure adds significant analytic value to the increasingly popular CityGML model.