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 unit spheres |
Maximum radius of inner spheres[1] | Optimality | Diagram |
|---|---|---|---|
| 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
- ↑ 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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