Two combinatorial properties of a class of simplicial polytopes
- Cite this article as:
- Lee, C.W. Israel J. Math. (1984) 47: 261. doi:10.1007/BF02760600
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Letf(Psd) be the set of allf-vectors of simpliciald-polytopes. ForP a simplicial 2d-polytope let Σ(P) denote the boundary complex ofP. We show that for eachf ∈f(Psd) there is a simpliciald-polytopeP withf(P)=f such that the 11 02 simplicial diameter of Σ(P) is no more thanf0(P)−d+1 (one greater than the conjectured Hirsch bound) and thatP admits a subdivision into a simpliciald-ball with no new vertices that satisfies the Hirsch property. Further, we demonstrate that the number of bistellar operations required to obtain Σ(P) from the boundary of ad-simplex is minimum over the class of all simplicial polytopes with the samef-vector. This polytopeP will be the one constructed to prove the sufficiency of McMullen's conditions forf-vectors of simplicial polytopes.