The aim of this paper is to present the first part of a new approach devoted to the generation of a data structure and operators for the hierarchical representation of 3D polyhedra. Here are described the treatments which allow to create some of the elements of this hierarchical model. At first, partitions of the initial polyhedron are mapped into planar connex hulls. Then, these domains are used like a piecewise parametric 2D space for subsequent polyhedra generations. In order to create such a mapping, the initial 3D polyhedron is partitioned to produce simply convex subsets which can be submitted to the parametrization process. The next step consists in the generation of a minimum representation of the initial 3D polyhedron. This representation forms the root of the hierarchical data structure. Then, the mapping obtained allows the construction of various polyhedral representations of the initial geometry. Criteria related to 3D parameters are used to generate the range of polyhedra. The reverse mapping (from 2D to 3D) helps reduce the computing cost required to generate 3D polyhedra. Each 3D polyhedron generation is carried out under 3D geometric criteria depending on the context. i.e.: structural analysis, levels of details of a geometric model, ... Among the goals of the hierarchical data structure, the unification and the inter dependency of the meshes required to carry out the structural analysis of a part occupies a central position.