We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond 12, which previous methods could not achieve. The new algorithm is applied to the Coxeter-Todd lattice $K_{12}$ as well as to a family of lattices obtained from laminating $K_{12}$. By optimizing this family, we obtain a new best 13-dimensional lattice quantizer (among the lattices with published exact quantizer constants).
翻译：我们提出了一种算法，用于精确计算具有已知对称群的格子的 Voronoi 单元。我们的算法与面的总数成比例超线性增长，并适用于维度超过 12 的情况，而以前的方法无法实现。我们将新算法应用于 Coxeter-Todd 格子 $K_{12}$ 以及从 $K_{12}$ 层压得到的一组格子。通过优化该族格子，我们获得了一个新的最佳 13 维格子量化器（在已发表的具有精确量化器常数的格子中）。
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