Abstract. We present an orthogonal topological framework which is able to provide incidence traversal operations for all topological elements. The run-time performance of this topological traversal operations can be optimized at a highly expressive level, where the abstraction penalty imposed by this approach is negligible. For the topological storage we use vertex-cell as well as cell-vertex incidence information. Using metaprogramming and the archetype concept we can optimize traversal of inter-dimensional objects without explicitly storing them. 