M Theory Lesson 294

Recall that the associahedra polytopes are labeled by chorded polygons. For example, the vertices and edges of the pentagon (the associahedron in the plane) are given as a five sided polygon with either one or two chords. In category theory, the edges of the associahedron may be directed. This can be achieved by choosing a root edge on the index polygon, which is the same as selecting a root for the dual tree. A natural source (target) for the full polytope is then given by the fully left (right) branching tree. But for many purposes, where the cyclic symmetry is relevant, we need not select a root edge.