Sphere packing in a sphere

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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
unit spheres
Maximum radius of inner spheres[1] Optimality Diagram
1 1.0000 Trivially optimal. Spheres in sphere 01.png
2 0.5000 Trivially optimal. Spheres in sphere 02.png
3 0.4641... Trivially optimal. Spheres in sphere 03.png
4 0.4494... Proven optimal. Spheres in sphere 04.png
5 0.4142... Proven optimal. Spheres in sphere 05.png
6 0.4142... Proven optimal. Spheres in sphere 06.png
7 0.3859... Proven optimal. Spheres in sphere 07.png
8 0.3780... Proven optimal. Spheres in sphere 08.png
9 0.3660... Proven optimal. Spheres in sphere 09.png
10 0.3530... Proven optimal. Spheres in sphere 10.png
11 0.3445... Proven optimal. Spheres in sphere 11.png
12 0.3445... Proven optimal. Spheres in sphere 12.png

References[edit]

  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.