Triangulation is the division of a surface into a set of Triangles, usually with the restriction that each Triangle side is entirely shared by two adjacent Triangles. It was proved in 1930 that every surface has a triangulation, but it might require an infinite number of Triangles. A surface with a finite number of triangles in its triangulation is called Compact. B. Chazelle showed that an arbitrary Simple Polygon can be triangulated in linear time.
See also Compact Surface, Delaunay Triangulation, Japanese Triangulation Theorem, Simple Polygon