Computing surface and/or object intersections is a cornerstone of many algorithms in Geometric Modeling and Computer Graphics, for example Set Operations between solids, or surface Ray Casting display. We present an object centered, information preserving, hierarchical representation for polyhedra called Prism Tree. We use the representation to decompose the intersection algorithms into two steps: the localization of intersections, and their processing. When dealing with polyhedra with many faces (typically more than one thousand), the first step is by far the most expensive. The Prism Tree structure is used to compute efficiently this localization step. A preliminary implementation of the Set Operations and Ray casting algorithms has been constructed.