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Abstract: The second and fourth authors have conjectured that a certain hollow tetrahedron of width 2+ 2 attains the maximum lattice width among all three-dimensional convex bodies. We here prove a local version of this conjecture: there is a neighborhood U of in the Hausdorff distance such that every convex body in U \ { } has width strictly smaller than . When the search space is restricted to tetrahedra, we compute an explicit such neighborhood. We also limit the space of possible counterexamples to the conjecture. We show, for example, that their width must be smaller than 3.972 and their volume must lie in [2.653,19.919].
Fuente: Discrete Applied Mathematics, 2021, 298, 129-142
Publisher: North-Holland
Publication date: 31/07/2021
No. of pages: 14
Publication type: Article
DOI: 10.1016/j.dam.2021.04.009
ISSN: 0166-218X
Spanish project: MTM2017-83750-P
Publication Url: https://doi.org/10.1016/j.dam.2021.04.009
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AVERKOV, GENNADIY
CODENOTTI, GIULIA
MACCHIA, ANTONIO
FRANCISCO SANTOS LEAL
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