In many applications it is important that one view a scene at different levels of detail. A prime example is flight simulation. A high level of detail is needed when flying low, whereas a low level of detail suffices when flying high. More precisely, one would like to visualize the part of the scene that is close at a high level of detail and the part that is far away at a low level of detail. We propose a hierarchy of detail levels for a polyhedral terrain (or, triangulated irregular network) that given a viewpoint, makes it possible to select the appropriate level of detail for each part of the terrain in such a way that the parts still fit together. The main advantage of our structure is that it uses the Delaunay triangulation at each level, so that triangles with very small angles are avoided. This is the first method that uses the Delaunay triangulation and still allows one to combine different levels into a single representation.