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为球体填充的体积的分数。在三个维度中，对于相同的球体，有三种周期性堆积：立方晶格、面心立方晶格和六方晶格。开普勒在 1611 年假设，密堆积（立方或六方，它们具有等效的堆积密度）是可能的最密堆积，这一论断被称为开普勒猜想。因此，寻找球体最密堆积（不一定是周期性的）的问题被称为开普勒问题，其中
满足
。
维超球面）的最大数量称为 
维亲吻数。
(Gardner 1966)，明显低于 Hilbert 和 Cohn-Vossen (1999, p. 51) 报告的值。要保持刚性，每个球体必须接触至少四个其他球体，并且这四个接触点不能在单个半球中或全部在一个赤道上。
。这是金刚石中的碳原子形成的晶格 (Conway and Sloane 1993, p. 113)。
、12 以及所有从 
从 
到 
的情况，除了 
，并且几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.