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Densest packings of two translates of a lattice in five dimensions

Contributed by Deep Bhattacharjee, Ushashi Bhattacharya

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.

A mix of human-written and AI-generated textHuman understanding: some parts$D_5$ latticeRyshkov polyhedronSphere packingVoronoi celldeep holeperiodic packing

Oct 22, 2026PDF ↗View work →

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Densest packings of two translates of a lattice in five dimensions

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