Triangulation

Summary

A triangulation of a topological space is a homeomorphism from the geometric realization of a simplicial complex onto the space. It cuts the space into vertices, edges, triangles and their higher-dimensional analogues, glued along faces. Triangulations turn topological questions into combinatorial ones, which is how simplicial homology and the Euler characteristic were first computed. Whether every manifold can be triangulated, and whether triangulations are essentially unique, are classical questions of geometric topology.