Three non-equivalent realizations of the associahedron

Abstract

We review three realizations of the associahedron that arise as secondary polytopes, from cluster algebras, and as Minkowski sums of simplices, and show that under any choice of parameters, the resulting associahedra are affinely non-equivalent.

12 pages, 9 figures. The results of this preprint have been included in a more comprehensive paper, jointly with Francisco Santos, arXiv:1109.5544