数几何中的一种新算法

4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI:10.1109/ISVD.2007.6

M. D. Sikirić, K. Rybnikov

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引用次数: 5

摘要

如果一个晶格Delaunay多面体P的Delaunay球是围绕P限定的唯一椭球，则称其为完美多面体P。我们的方法克服了以前使用的方法的主要缺点[Du05]。我们已经实现并使用了我们的算法来寻找维度6,7,8的完美Delaunay多面体。我们的发现导致了一个新的猜想，揭示了晶格德劳内瓷砖的结构。

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A New Algorithm in Geometry of Numbers

A lattice Delaunay polytope P is called perfect if its Delaunay sphere is the only ellipsoid circumscribed about P. We present a new algorithm for finding perfect Delaunay polytopes. Our method overcomes the major shortcomings of the previously used method [Du05]. We have implemented and used our algorithm for finding perfect Delaunay polytopes in dimensions 6, 7, 8. Our findings lead to a new conjecture that sheds light on the structure of lattice Delaunay tilings.

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4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)

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