Geodesic
Klein polyhedra and relative minima of lattices
Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 546-552

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We prove that in $\mathbb R^3$, the relative minima of almost any lattice belong to the surface of the corresponding Klein polyhedron. We also prove, for almost any lattice in $\mathbb R^3$, that the set of relative minima with nonnegative coordinates coincides with the union of the set of extremal points of the Klein polyhedron and a set of special points belonging to the triangular faces of the Klein polyhedron. 
@article{MZM_2006_79_4_a4,
     author = {O. N. German},
     title = {Klein polyhedra and relative minima of lattices},
     journal = {Matemati\v{c}eskie zametki},
     pages = {546--552},
     publisher = {mathdoc},
     volume = {79},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a4/}
}
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O. N. German. Klein polyhedra and relative minima of lattices. Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 546-552. http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a4/