Sphere packing in a sphere
From Infogalactic: the planetary knowledge core
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. | 120px |
| 2 | 0.5000 | Trivially optimal. | 120px |
| 3 | 0.4641... | Trivially optimal. | 120px |
| 4 | 0.4494... | Proven optimal. | 120px |
| 5 | 0.4142... | Proven optimal. | 120px |
| 6 | 0.4142... | Proven optimal. | 120px |
| 7 | 0.3859... | Proven optimal. | 120px |
| 8 | 0.3780... | Proven optimal. | 120px |
| 9 | 0.3660... | Proven optimal. | 120px |
| 10 | 0.3530... | Proven optimal. | 120px |
| 11 | 0.3445... | Proven optimal. | 120px |
| 12 | 0.3445... | Proven optimal. | 120px |
References
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