Stasheff polytopes and the coordinate ring of the cluster X-variety of   type A_n
  We define Stasheff polytopes in the space of tropical points of cluster A-varieties. We study the supports of products of elements of canonical bases for cluster X-varieties. We prove that, for the cluster X-variety of type A_n, such supports are Stasheff polytopes. 
Linhui Shen
math.AG