Title :
A New Algorithm in Geometry of Numbers
Author :
Dutour, Mathieu ; Rybnikov, Konstantin
Author_Institution :
Rudjer Boskovic Inst., Zagreb
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.
Keywords :
computational geometry; mesh generation; Delaunay sphere; lattice Delaunay polytope; lattice Delaunay tiling; Ellipsoids; Geometry; Laboratories; Lattices; Slabs; Zinc;
Conference_Titel :
Voronoi Diagrams in Science and Engineering, 2007. ISVD '07. 4th International Symposium on
Conference_Location :
Glamorgan
Print_ISBN :
0-7695-2869-4
DOI :
10.1109/ISVD.2007.6
