In this paper we discuss a geometrical data base that includes three different geometrical representations of one and the same reconstructed 3D shape: the contour-pile, the voxel enumeration, and the triangulation of a surface. The data base is tailored for 3D shapes obtained from plan-parallel serial sections. It is explained how this geometrical data base is useful with the different processing approaches of a 3D shape, such as analysis and visualisation. Methods of conversion between the geometrical representations are discussed. Examples of the operation of the data base as it is embedded in a data base management system are given by illustrations of retrieval of geometrical information.