Topological information is a promising resource to research in shape-understanding as it provides a high-level description of the characteristics of a shape, and such high-level description often has strong association with the semantics of an object. The Shape Acquisition and Processing (SAP) ontology has been designed to maintain useful information of a model. We propose here an extension to the SAP ontology, that addresses the non-manifold properties of a model. Useful information about the connectivity of an object can be obtained based on an analysis of its non-manifold properties, because the structure of a non-manifold object can be considered as a graph of manifold parts connected together at non-manifold joints. The manifold parts are often pieces that have strong semantic associations. In this work, we describe the type of non-manifold properties, the various types of connected components in a non-manifold object and their semantical significance. We address how the Euler’ characteristics of a non-manifold object can be found based on such information. All such information are extractable from a model using TopMesh, a tool that we have developed. In this work, we also describe the features of TopMesh, namely, all the topological properties it extracts.