Face Pairing Descriptions of 3-manifolds

3-manifold is a topological space that locally looks like Euclidean 3-dimensional space. Finding a global understanding of a 3-manifold, however, is much more difficult. Here we describe the face pairing identification which provides a combinatorial characterization of a 3-manifold and go on to consider how small changes in a given pairing results in significant changes to the manifold.