A multitriangulation of order k, or a k-triangulation, of a convex n-gon is a maximal set of diagonals such that no k+1 of them mutually cross in the interior of the n-gon. First studied in the 1992 paper “A Turán-Type Theorem on the Chords of Convex Polygons” by Capoyleas and Pach, k-triangulations have recently been studied in the context of the multi-associahedron. In this talk, we will prove a result by Pilaud and Santos in the paper “Multi-triangulations as Complexes of Star Polygons”, namely, that k-triangulations are formed by a union of k-stars and “k-irrelevant” edges. Time permitting, we will also discuss our recent work concerning the realization of the multi-associahedron.