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I believe that all facets of a Voronoi-cell of a lattice are centerally symmetric. Is my argument correct? Is this true?
So let $L$ be a full dimensional lattice in $\mathbb{R}^{n}$. Then the Voronoi-cell of the lattice are precisely the points in $\mathbb{R}^{n}$ that are at least as close to the origin, as to any ...
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How to construct lattices with largest possible number of Voronoi relevant lattice vectors?
Let M be the generator matrix of a $N$ dimensional lattice, and $V$ the set of Voronoi relevant vectors. The Voronoi cell for the origin can be written as $\text{Vor}_{\bf 0}(M)=\left\{{\bf x}: |{\bf ...