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

Lee, Carl W.

Eur. J. Comb. 10, No. 6, 551-560 (1989).

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.

Reviewer: Jörg M. Wills (Siegen)

MSC:

52B99

Polytopes and polyhedra

Keywords:

convex polytopes

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