{"title":"A New Algorithm in Geometry of Numbers","authors":"M. D. Sikirić, K. Rybnikov","doi":"10.1109/ISVD.2007.6","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISVD.2007.6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
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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