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Kalai's squeezed three-spheres are polytopal
Pfeifle, Julián
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
In 1988, Kalai [5] 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 [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.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Polytopes
Hamiltonian graph theory
Combinatory logic
Convex geometry
Politops
Lògica combinatòria
Geometria convexa
Hamilton, Sistemes de
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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