Given a graph Γ, we construct a simple, convex polytope, dubbed graph-associahedra, whose face poset is based on the connected subgraphs of Γ. 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. © 2005 Elsevier B.V. All rights reserved.
Carr, M., & Devadoss, S. L. (2006). Coxeter complexes and graph-associahedra. Topology and Its Applications, 153(12), 2155–2168. https://doi.org/10.1016/j.topol.2005.08.010