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為球體填充的體積的分數。在三個維度中，對於相同的球體，有三種週期性堆積：立方晶格、面心立方晶格和六方晶格。開普勒在 1611 年假設，密堆積（立方或六方，它們具有等效的堆積密度）是可能的最密堆積，這一論斷被稱為開普勒猜想。因此，尋找球體最密堆積（不一定是週期性的）的問題被稱為開普勒問題，其中
滿足
。
維超球面）的最大數量稱為 
維親吻數。
(Gardner 1966)，明顯低於 Hilbert 和 Cohn-Vossen (1999, p. 51) 報告的值。要保持剛性，每個球體必須接觸至少四個其他球體，並且這四個接觸點不能在單個半球中或全部在一個赤道上。
。這是金剛石中的碳原子形成的晶格 (Conway and Sloane 1993, p. 113)。
、12 以及所有從 
從 
到 
的情況，除了 
，並且幾乎可以肯定是最佳的。
." Math. 33, 137-147, 1986.Muder, D. J. "Putting the Best Face of a Voronoi Polyhedron." Proc. London Math. Soc. 56, 329-348, 1988.Rogers, C. A. "The Packing of Equal Spheres." Proc. London Math. Soc. 8, 609-620, 1958.Rogers, C. A.