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I would like to find the N points inside a given sphere that maximises the minimum distance between any two.

In other words, how can I position N equal (unit) spheres inside a larger sphere, as they stay as distant as possible?

Could anybody give me a hint or a reference please?

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You're actually asking two different questions here. For the first one, points in a sphere, the optimal configuration will scale with the radius of the given sphere, so no harm in assuming the sphere has radius 1. In the second question, the radius of the larger sphere matters --- if it's too small, you won't be able to put $N$ unit spheres inside it at all, while if it's very large, they'll all be crowded up against the outside. Anyway, two websites that might be worth a look are Erich's Packing Center and the Geometry Junkyard. –  Gerry Myerson Sep 30 '12 at 12:51

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