Kalai's squeezed 3-spheres are polytopal
| dc.creator | Pfeifle, Julian | |
| dc.date | 2001-10-22 | |
| dc.date.accessioned | 2026-07-07T04:44:00Z | |
| dc.date.available | 2026-07-07T04:44:00Z | |
| dc.description | In 1988, Kalai extended a construction of Billera and Lee to produce many triangulated (d-1)-spheres. In fact, in view of upper bounds on the number of simplicial d-polytopes by Goodman and Pollack, 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. Moreover, we can now give a shorter proof of Hebble & Lee's 2000 result that the dual graphs of these 4-polytopes are Hamiltonian. Therefore, the polars of these Kalai polytopes yield another family supporting Barnette's conjecture that all simple 4-polytopes admit a Hamiltonian circuit. | |
| dc.description | 11 pages, 5 figures; accepted for publication in J. Discrete & Computational Geometry | |
| dc.identifier | https://arxiv.org/abs/math/0110240 | |
| dc.identifier | http://arxiv.org/abs/math/0110240 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62463 | |
| dc.subject | Combinatorics | |
| dc.title | Kalai's squeezed 3-spheres are polytopal | |
| dc.type | text |