2007/02/06 by Mathieu Dutour Sikirić, Mathieu Dutour, Dutour, Mathieu +4
Computer Science · Mathematics · #11-xx #52Bxx #52Cxx #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT) #Point processes and geometric inequalities #math.MG #math.NT #msc:11-xx #msc:52Bxx #msc:52Cxx
paper · pdf · doi:10.48550/arxiv.math/0702136
44 pages
arxiv created 2007/02/06 · openalex publication_date 2007/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A lattice Delaunay polytope is known as perfect if the only ellipsoid, that can be circumscribed about it, is its Delaunay sphere. Perfect Delaunay polytopes are in one-to-one correspondence with arithmetic equivalence classes of positive quadratic functions on the n-dimensional integral lattice that can be recovered, up to a scale factor, from the representations of its minimum. We develop a structural theory of such polytopes and describe all known perfect Delaunay polytopes in dimensions one through eight. We suspect that this list is complete.