In this paper, we introduce the progressive simplicial complex (PSC) representation, a new format for storing and transmitting triangu- lated geometric models. Like the earlier progressive mesh (PM) representation, it captures a given model as a coarse base model together with a sequence of refinement transformations that pro- gressively recover detail. The PSC representation makes use of a more general refinement transformation, allowing the given model to be an arbitrary triangulation (e.g. any dimension, non-orientable, non-manifold, non-regular), and the base model to always consist of a single vertex. Indeed, the sequence of refinement transforma- tions encodes both the geometry and the topology of the model in a unified multiresolution framework. The PSC representation retains the advantages of PM's. It defines a continuous sequence of approx- imating models for runtime level-of-detail control, allows smooth transitions between any pair of models in the sequence, supports progressive transmission, and offers a space-efficient representa- tion. Moreover, by allowing changes to topology, the PSC sequence of approximations achieves better fidelity than the corresponding PM sequence.