  In this paper, we prove that the set of triangulations of a polygon can be
equipped with an order to become a lattice. First, we define this order. In
[HN99], authors defined the flip operator and then prove some properties of the
graph of triangulations. We use their theorems and extend them to construct the
lattice of triangulations. We prove this lattice property and introduce an
elegant algorithm which correctness is induced from the proof. The complexity
of this algorithm will be considered. This algorithm is efficient to find the
infimum of a pair of triangulations.
