Authors: Julian Pfeifle Günter M Ziegler
Publish Date: 2004/10/15
Volume: 330, Issue: 4, Pages: 829-837
Abstract
We construct Open image in new window combinatorial types of triangulated 3spheres on n vertices Since by a result of Goodman and Pollack 1986 there are no more than 2On log n combinatorial types of simplicial 4polytopes this proves that asymptotically there are far more combinatorial types of triangulated 3spheres than of simplicial 4polytopes on n vertices This complements results of Kalai 1988 who had proved a similar statement about dspheres and d+1polytopes for fixed d≥4
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