Triangulation of a simple polygon $P$ is a decomposition of $P$ into triangles by a maximal set of non-intersecting diagonals. We also know that triangulation of a polygon is not neccessarily unique. The question (taken from Computational Geometry in C by J. Rourke):
Which polygons have the fewest number of distinct triangulations? Can polygons have unique triangulations? Which polygons have the largest number of distinct triangulations?
Note: I've already answered the second part by drawing a convex 4-gon with only 1 possible diagonal. The problem is the other two parts.