The very first description of an associahedron is to be found in the Ph. D. thesis of the topologist Jim Stasheff, but he was unable to represent it as a strict polytope. Instead, he had to be content with a somewhat curvy shape. [...] Of course, it is easy to see how to modify this to be a true polytope. In fact, John Milnor showed up at Stasheff's thesis defense with a cardboard model. But is is not at all easy to see how to straighten out Stasheff's curvy associahedron in all dimensions.