  The associahedron is a convex polytope whose face poset is based on
nonintersecting diagonals of a convex polygon. In this paper, given an
arbitrary simple polygon P, we construct a polytopal complex analogous to the
associahedron based on convex diagonalizations of P. We describe topological
properties of this complex and provide realizations based on secondary
polytopes. Moreover, using the visibility graph of P, a deformation space of
polygons is created which encapsulates substructures of the associahedron.
