Manual indexing of large databases of geometric information is costly and often impracticable. Because of this research into retrieval and indexing schemes has focused on the development of various 3D to 2D mappings that characterise a shape as a histogram with a small number of parameters. Many methods of generating such 2D signatures (i.e. histograms) have been proposed, generally based on geometric measures of say curvature or distance. However these geometric signatures lack information about topology and tend to become indistinct as the complexity of the shape increases. This paper describes a new method for characterising both the geometry and topology of shapes in a single 2D graph, the Surface Partitioning Spectrum (SPS). We evaluate the effectiveness of using the SPS with a Neural Network to assess the similarity of shapes within a test set.