<P> A vertex of a plane tiling or tessellation is a point where three or more tiles meet; generally, but not always, the tiles of a tessellation are polygons and the vertices of the tessellation are also vertices of its tiles . More generally, a tessellation can be viewed as a kind of topological cell complex, as can the faces of a polyhedron or polytope; the vertices of other kinds of complexes such as simplicial complexes are its zero - dimensional faces . </P> <P> A polygon vertex x of a simple polygon P is a principal polygon vertex if the diagonal (x, x) intersects the boundary of P only at x and x . There are two types of principal vertices: ears and mouths . </P> <P> A principal vertex x of a simple polygon P is called an ear if the diagonal (x, x) that bridges x lies entirely in P. (see also convex polygon) According to the two ears theorem, every simple polygon has at least two ears . </P> <P> A principal vertex x of a simple polygon P is called a mouth if the diagonal (x, x) lies outside the boundary of P . </P>

Point is the vertex of the angle marked in the figure