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 the dual graphs of these 4 -polytopes are Hamiltonian.
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Received February 12, 2001, and in revised form October 19, 2001. Online publication March 4, 2002.
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Pfeifle, J. Kalai’s Squeezed 3-Spheres Are Polytopal. Discrete Comput Geom 27, 395–407 (2002). https://doi.org/10.1007/s00454-001-0074-3
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DOI: https://doi.org/10.1007/s00454-001-0074-3