Converting surfaces into a volume has a long interest in several communities, e.g. the computational mechanics community. This process involves having specific surfaces which can be converted into a solid, i.e., a volume. This paper presents in a clear and brief manner the topological properties conserved during surface to volume transformation. We state the limits of this approach if a specific volume structure is required. Volume structures can be a coarse volume organization or meshes. For that purpose, surface manifolds are mathematically turned into a volume manifold. Topological tools are presented to understand which properties are transmitted to the volume and which ones are unset. Developments are submitted both for continuous and discrete manifolds using CW-complexes.