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Smooth centrally symmetric polytopes in dimension 3 are IDP

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arxiv 1802.01046 v2 pith:J3A5BTJF submitted 2018-02-03 math.CO math.AG

Matthias Beck , Christian Haase , Akihiro Higashitani , Johannes Hofscheier , Katharina Jochemko , Lukas Katthän , Mateusz Micha{l}ek This is my paper · ORCID
classification math.COmath.AG
keywords centrallylatticepolytopessmoothsymmetricconjectureconjecturedcovered
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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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