volume 27, issue 3, P395-407 2002
DOI: 10.1007/s00454-001-0074-3
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Abstract: In 1988 Kalai [5] extended a construction of Billera and Lee to produce many triangulated (d −1)-spheres. In fact, in view of the upper bounds on the number of simplicial d-polytopes by Goodman and Pollack [2], [3], he derived that for every dimension d ≥ 5, most of these (d −1)-spheres are not polytopal. However, for d = 4, this reasoning fails. We can now show that, as already conjectured by Kalai, all of his 3-spheres are in fact polytopal.We also give a shorter proof for Hebble and Lee's result [4] that t…

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