Configuration spaces, Coxeter operads, and graph-associahedra

We look at natural generalizations of the Deligne-Mumford compactification of the real moduli space of Riemann spheres. They inherit a tiling by the graph-associahedra convex polytopes. Based on explicit configuration space models of classical Coxeter complexes, a Fulton-MacPherson compactification of these spaces is described and then used to demonstrate the underlying Coxeter operad structure.