Triangulation is the division of a surface or plane polygon into a set of triangles, usually with the restriction that each triangle side is entirely shared by two adjacent triangles. It was proved in 1925 that every surface has a triangulation, but it might require an infinite number of triangles and the proof is difficult. A surface with a finite number of triangles in its triangulation is called compact.

art gallery theorem | circumcenter of mass | compact surface | Delaunay triangulation | Japanese theorem | simple polygon | tessellation | triangulation point