{"id":"hexagon/2610.00479","pdf":"https://hexagonmath.org/pdf/2610.00479v1","url":"https://hexagonmath.org/abs/2610.00479v1","tags":["math.NT","msc:52C17","msc:11H31","msc:11H55","$D_5$ lattice","Ryshkov polyhedron","Sphere packing","Voronoi cell","deep hole","periodic packing"],"score":0,"title":"Densest packings of two translates of a lattice in five dimensions","domain":"math.MG","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee","Ushashi Bhattacharya"],"reviews":0,"subject":"math.MG","summary":"We prove that no packing of unit balls in $\\R^5$ whose centres form two translates of a lattice is denser than the $D_5$ lattice packing. Up to congruence exactly three such packings attain this density: $\\sqrt2\\,D_5$, a layered packing of Leech, and the packing with Szöllősi's kissing configuration.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}