Polyhedral models are widely used for applications such as manufacturing, digital simulation or visualization. They are discrete models; easy to store, to manipulate, allowing levels of resolution for visualization. They can be easily exchanged between CAD systems without loss of data. Previous works (Comput Aided Des 29(4):287-298, 1997, Comput Graphics 22(5):565-585, 1998) have focused on simplification process applied to polyhedral part models. The goal of the proposed approach is to extend these processes to polyhedral assembly models, describing the digital mock-up of a future manufacturing product. To apply simplification techniques or other processes on polyhedral assemblies, contact surfaces between interacting objects have to be identified and specific constraints must be applied for processing. The approach proposed allows checking and maintaining a global consistency of the assembly model to ensure the reliability of the future processes. Thus, contacts between objects are detected using an approach that works for a static configuration of the assembly. Finally, a precise detection of the faces involved in each contact area is made and the resulting input domains identified are processed using a local Frontal Delaunay re-meshing technique to produce an identical tessellation on both objects involved in the processed contact. The quality of the triangulation produced is also checked.