What is "associahedron"

n. (context mathematics English) A convex polytope in which each vertex corresponds to a way of correctly inserting opening and closing parentheses in a word of ''n'' letters and the edges correspond to a single application of the associativity rule.

In mathematics, an associahedron K is an (n − 2)-dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening and closing parentheses in a word of n letters and the edges correspond to single application of the associativity rule. Equivalently, the vertices of an associahedron correspond to the triangulations of a regular polygon with n + 1 sides and the edges correspond to edge flips in which a single diagonal is removed from a triangulation and replaced by a different diagonal. Associahedra are also called Stasheff polytopes after the work of Jim Stasheff, who rediscovered them in the early 1960s after earlier work on them by Dov Tamari.