Sphere packing in a sphere

Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It is the three-dimensional equivalent of the circle packing in a circle problem in two dimensions.

Number of
inner spheres		 Maximum radius of inner spheres[1] Optimality Diagram
Exact form Approximate
1 1.0000 Trivially optimal.
2 0.5000 Trivially optimal.
3 0.4641... Trivially optimal.
4 0.4494... Proven optimal.
5 0.4142... Proven optimal.
6 0.4142... Proven optimal.
7 0.3859... Proven optimal.
8 0.3780... Proven optimal.
9 0.3660... Proven optimal.
10 0.3530... Proven optimal.
11 0.3445... Proven optimal.
12 0.3445... Proven optimal.

References

  1. ↑ Pfoertner, Hugo (2008-02-02). "Densest Packings of n Equal Spheres in a Sphere of Radius 1. Largest Possible Radii". Archived from the original on 2012-03-30. Retrieved 2013-11-02.
  • Huang, WenQi; Yu, Liang (2012). "Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem". arXiv:1202.4149.
  • Gensane, T. (2003). "Dense packings of equal spheres in a larger sphere". Les Cahiers du LMPA J. Liouville. 188.
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