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The conjecture on densest congruent geodesic ball packings in Thurston geometries
About 4 years old
Densest-arrangement conjecture. The ball arrangement $\mathcal{B}_{\mathrm{opt}}(R_4,K_4)$ provides the densest congruent geodesic ball packing for the Thurston geometries.
openball-packings thurston-geometries
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The conjecture on densest congruent geodesic ball packings in Thurston geometries