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The associahedron and triangulations of the \(n\)-gon. (English) Zbl 0682.52004

For a convex \(n\)-gon \(P_n\), \(n\geq 3\), in the plane let \(\Sigma_n\) denote the collection of all sets of mutually noncrossing diagonals of \(P_n\). The author proves that \(\Sigma_n\) is isomorphic to the boundary complex of some \((n-3)\)-dimensional simplicial convex polytope, and that this polytope can be geometrically realized with the dihedral group \(D_n\) as its symmetry group.

MSC:

52B99 Polytopes and polyhedra
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