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Given a (3D) cuboid and an integer N, how can I position N spheres that fit inside without touching such that the radius of the spheres is maximised?

Is there some group theory that I need to know, or are there "jiggling" algorithms that can calculate an answer?

Actually, only the centres of the spheres need to be inside. If I was concerned with a cube I think I could get away with scaling the solution after it was found, however I'm not sure if that's possible.

Put another way, I would like to find the N points inside a given cuboid that maximises the minimum distance between any two.

What algorithm does this use? Can this be adapted?

This link to wikipedia is infuriating...

If an algorithm or general method that finds the optimal solution is not known or does not exist, is there one that will find a approximate or "good enough" solution?

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You may find something useful at – Gerry Myerson Sep 13 '12 at 12:14
Also of possible interest, – Gerry Myerson Sep 13 '12 at 12:17
My apologies, I have corrected the first paragraph. I've seen your first link, and basically wish to 1. Replicate the calculations they made, 2. Generalise to spheres in a cuboid, 3. Correct to allow the spheres outside iff their centres remain inside. The 2nd link looks useful, I will check it for information on the algorithms/methods used. Edit: From your 1st link: Mentions the "Billiard algorithm" and how it was adapted. This may be what I am after, I will give it a read. – Dijkstra Sep 13 '12 at 14:05
Allowing part of the sphere outside the cuboid doesn't change the problem: increase the dimensions $2r$ in each dimension and demand the entire sphere is inside is the same. – Ross Millikan Sep 13 '12 at 14:17
My question is the same, but for spheres. In other words, I would like to find the N points inside a given sphere that maximises the minimum distance between any two. How can I position N equal spheres inside a larger sphere, as they stay as distant as possible? Could anybody give me a hint or a reference please? – tSirmen Sep 20 '12 at 11:14

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