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Coxeter complexes and graph-associahedra. (English) Zbl 1099.52001
The authors suggest a construction of a simple convex polytope, called graph-associahedra, which is associated with a given graph ${\Gamma }$ and whose face partial order coincides with the partial order of sets of connected subgraphs of ${\Gamma }$. This construction includes as particular cases the Stasheff associahedron and the Bott-Taubes cyclohedron. In case of simplicial Coxeter groups and respective Coxeter complexes the graph-associahedron represents its fundamental domain. Furthermore, the minimal blow-ups of such Coxeter complexes have tiling by graph-associahedra, which can be viewed as a generalization of the Deligne-Knudsen-Mumford compactification of the real moduli space of rational curves with marked points.

##### MSC:
 52B05 Combinatorial properties of convex sets 05B45 Tessellation and tiling problems 05C70 Factorization, etc.
minimal blow-ups