Mouth

A Principal Vertex $x_i$ of a Simple Polygon $P$ is called a mouth if the diagonal $[x_{i-1}, x_{i+1}]$ is an extremal diagonal (i.e., the interior of $[x_{i-1}, x_{i+1}]$ lies in the exterior of $P$).

See also Anthropomorphic Polygon, Ear, One-Mouth Theorem

References

Toussaint, G. ``Anthropomorphic Polygons.'' Amer. Math. Monthly 122, 31-35, 1991.