Is the Voronoi region of a lattice symmetric around origion?

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Assume an n-dimensional lattice. Is the Voronoi region of the lattice symmetric around origion?

In other word, is the following statement true? "if $x\in \mathcal{V}$ then $-x\in \mathcal{V}$" where $\mathcal{V}$ indicates the fundamental Voronoi region of the lattice.

Thanks,