  There exist natural generalizations of the real moduli space of Riemann
spheres based on manipulations of Coxeter complexes. These novel spaces inherit
a tiling by the graph-associahedra convex polytopes. We obtain explicit
configuration space models for the classical infinite families of finite and
affine Weyl groups using particles on lines and circles. A Fulton-MacPherson
compactification of these spaces is described and this is used to define the
Coxeter operad. A complete classification of the building sets of these
complexes is also given, along with a computation of their Euler
characteristics.
