The Secondary Polytope: Digging for Combinatorial links between Triangulations and Polytopes (with
We review some of the most important definitions and interesting combinatorial result about triangulations. First, We present a clever connection between the Catalan numbers and the n-gon triangulations. Then, we explore some combinatorial isomorphisms that we can build around triangulations such as Binary trees, parenthesization, and the Associahedron, in order to give a good first look about the subject and it potential. Finally, we generalize the role of the Associahedron introducing the well-known Secondary Polytope.
