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Possible Duplicate:
well separated points on sphere

I have never studied geometry, but I assume there is a straightforward solution to this problem. In $\mathbb{R}^n$ I'd like to distribute $N$ points around the unit (n)-sphere surface, so that the points are evenly spaced (or more precisely, so that the minimum of pairwise distances between points is a maximum).

If $n$ were only $2$, then points would have the form $(\cos \frac{2\pi j}{N}+\phi, \sin \frac{2\pi j}{N}+\phi)$ with $j=1,\ldots,N$ and where $\phi$ is some rotational offset.

As another example, if $n=3$ and $N=8$, the solution is clearly the corners of a cube centred in the unit sphere. I suppose this would apply for any regular polyhedron.

However, I'm looking to do this for odd $N$, and ultimately with $n=N$.

Is there any way to extend the general solution for $n=2$ to higher dimensions?

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codebeard
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  • Searching "points" "sphere" gives many related/dup questions: http://math.stackexchange.com/questions/9846/which-tessellation-of-the-sphere-yields-a-constant-density-of-vertices/ http://math.stackexchange.com/questions/31619/well-separated-points-on-sphere – leonbloy Jan 11 '13 at 03:24
  • I did search thoroughly beforehand; forgive me if I didn't understand the terminology like 'tessellation' – codebeard Jan 11 '13 at 03:25
  • @leonbloy Actually, those don't seem to be duplicates. The first is about vertex density and I don't think it's going to apply for arbitrary $N$. The second does not require points to be evenly spaced (just well spaced). If you can point me to an actual answer, I'd be really happy. Otherwise, I don't think that's a good reason to vote down my question. – codebeard Jan 11 '13 at 03:31
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    "so that the minimum of pairwise distances between points is a maximum" Isn't that exactly this? What am I missing? – leonbloy Jan 11 '13 at 03:41

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