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How could I write an algorithm to generate n points distributed 'evenly' on a sphere? I already wrote an algorithm to generate points distributed uniformly on the surface (here), but by 'evenly' distributed I mean the way a bunch of electric charges might settle on the surface of a sphere, i.e. the minimum distance between any pair of points should be maximised. For n=2, it would just return any pair of polar opposite points. For n=32 it would probably look something like a soccerball tiling. For something general like n=7, I have no idea what it would look like although the problem still seems to me to be well-defined.

Is the problem equivalent whether the distance is measured on the surface or in the 3d space?

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wim
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  • Many related questions here, e.g., http://math.stackexchange.com/questions/66365/optimal-distribution-of-points-over-the-surface-of-a-sphere? and http://math.stackexchange.com/questions/165819/how-to-tile-a-sphere-with-points-at-an-even-density? where several more pointers are given. – Gerry Myerson Feb 11 '13 at 04:39
  • lots of food for thought .. so is the general case an unsolved problem, then? – wim Feb 11 '13 at 05:26
  • That's my impression. I haven't checked to see whether any of the links on this site mention http://www.math.niu.edu/~rusin/known-math/index/spheres.html which has many links that may be of interest – Gerry Myerson Feb 11 '13 at 06:09
  • There are only a few regular solids (i.e., points separated by fixed distances on the sphere). – vonbrand Feb 11 '13 at 12:10
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    The user presently known as ℝⁿ. has a list of questions on this topic in his profile. –  Feb 12 '13 at 00:23
  • Sounds to me like putting a bunch of charges on a sphere and running a generic optimization algorithm to minimize potential energy would do a decent job. – user2357112 Aug 14 '17 at 20:27

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