• 1 Laboratoire d'informatique Algorithmique : Fondements et Applications [Efrei]
• 2 Ecole Polytechnique Fédérale de Lausanne [EPFL]
• 3 Efrei [Efrei]
• 4 Efrei (Villejuif / Bordeaux) [Efrei]

Consider the triangulations of a convex polygon with $n$ vertices. In 1988, Daniel Sleator, Robert Tarjan, and William Thurston have shown that the flip distance of two such triangulations is at most $2n-10$ when $n$ is greater than 12 and that this bound is sharp when $n$ is large enough. They also conjecture that `"large enough'' means greater than 12. A proof of this conjecture was recently announced by the author. A sketch of this proof is given here, with emphasis on the intuitions underlying the construction of lower bounds on the flip distance of two triangulations.