High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, topology generalizes the notion of triangulation in a natural way as follows: A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h:Kto X. Triangulation is useful in determining the properties of a topological space. For example, one can compute homology and cohomology groups of a triangulated space using simplicial homology and cohomology theories instead of more complicated homology and cohomology theories. For topological manifolds, there is a slightly stronger notion of triangulation: a piecewise-linear triangulation (sometimes just called a triangulation) is a triangulation with the extra property that the link of any simplex is a piecewise-linear sphere.