Smooth Centrally Symmetric Polytopes in Dimension 3 are IDP

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Date
2019
Authors
Beck, Matthias
Haase, Christian
Higashitani, Akihiro
Hofscheier, Johannes
Jochemko, Katharina
Katthän, Lukas
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10.1007/s00026-019-00418-x
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Annals of Combinatorics ; 23 (2019), 2. - pp. 255-262. - Birkhäuser. - ISSN 0218-0006. - eISSN 0219-3094
Abstract
In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda’s conjecture for centrally symmetric 3-dimensional polytopes, by showing they are covered by lattice parallelepipeds and unimodular simplices.
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510 Mathematics
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Smooth lattice polytopes, Integer decomposition property, Oda’s conjecture, Central symmetry, 3-dimensional polytopes
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ISO 690BECK, Matthias, Christian HAASE, Akihiro HIGASHITANI, Johannes HOFSCHEIER, Katharina JOCHEMKO, Lukas KATTHÄN, Mateusz MICHALEK, 2019. Smooth Centrally Symmetric Polytopes in Dimension 3 are IDP. In: Annals of Combinatorics. Birkhäuser. 23(2), pp. 255-262. ISSN 0218-0006. eISSN 0219-3094. Available under: doi: 10.1007/s00026-019-00418-x
BibTex
@article{Beck2019Smoot-52209,
  year={2019},
  doi={10.1007/s00026-019-00418-x},
  title={Smooth Centrally Symmetric Polytopes in Dimension 3 are IDP},
  number={2},
  volume={23},
  issn={0218-0006},
  journal={Annals of Combinatorics},
  pages={255--262},
  author={Beck, Matthias and Haase, Christian and Higashitani, Akihiro and Hofscheier, Johannes and Jochemko, Katharina and Katthän, Lukas and Michalek, Mateusz}
}
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