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Except for Triangles, every Simple Polygon has at least two nonoverlapping Ears.
See also Ear, One-Mouth Theorem, Principal Vertex
References
Meisters, G. H. ``Principal Vertices, Exposed Points, and Ears.'' Amer. Math. Monthly 87,
284-285, 1980.
Toussaint, G. ``Anthropomorphic Polygons.'' Amer. Math. Monthly 122, 31-35, 1991.