Associahedron

(n − 2)-dimensional convex polytope
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Stasheff polytope
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Associahedron
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Wikipedia creation date
10/9/2008
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In mathematics, an associahedron Kn 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.
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Stasheff polytope
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