Geodesic
Normal polytopes and ellipsoids
The electronic journal of combinatorics, Tome 28 (2021) no. 4
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We show that: (1) unimodular simplices in a lattice 3-polytope cover a neighborhood of the boundary of the polytope if and only if the polytope is very ample, (2) the convex hull of lattice points in every ellipsoid in $\mathbb{R}^3$ has a unimodular cover, and (3) for every $d\geqslant 5$, there are ellipsoids in $\mathbb{R}^d$, such that the convex hulls of the lattice points in these ellipsoids are not even normal. Part (c) answers a question of Bruns, Michałek, and the author.
DOI : 10.37236/10338
Classification : 52B20, 11H06 
@article{10_37236_10338,
     author = {Joseph Gubeladze},
     title = {Normal polytopes and ellipsoids},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {4},
     doi = {10.37236/10338},
     zbl = {1475.52022},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10338/}
}
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Joseph Gubeladze. Normal polytopes and ellipsoids. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10338

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