Abstract
Let P n be a convex n -gon in the plane, n ⩾ 3. Consider Σ n , the collection of all sets of mutually non-crossing diagonals of P n . Then Σ n is a simplicial complex of dimension n − 4. We prove that Σ n is isomorphic to the boundary complex of some ( n − 3)-dimensional simplicial convex polytope, and that this polytope can be geometrically realized to have the dihedral group D n as its group of symmetries. Formulas for the f -vector and h -vector of this polytope and some implications for related combinatorial problems are discussed.
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