2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100815Given a graph G, we construct a simple, convex polytope whose face poset is based on the connected subgraphs of G. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The geometric and combinatorial properties of the complex as well as of the polyhedra are given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford compactification of the real moduli space of curves.18 pages, 9 figures; revised content and referencesQuantum AlgebraAlgebraic GeometryCombinatoricsPrimary 14P25, Secondary 05B45, 52B11text