The associahedron is a polytope whose vertices correspond to subdivisions of a polygon into triangles by its diagonals, and whose higher-dimensional faces correspond to coarser subdivisions. (Bijectively, we can say that its vertices correspond to ways of parenthesizing a product of several terms, and its edges correspond to applications of the associative rule, hence its name.) In this talk, we will sketch one of many ways to construct the associahedron, by way of a far more general method for parametrizing well-behaved subdivisions of any polytope. Speaker(s): Will Dana