Maximum number of points on a sphere

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How can I calculate the maximum number of points that can be placed on the surface of a unit sphere, if any two points wont be closer than 1 unit?

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1 Answer

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This is essentially the generalized Kissing Number Problem, where the center sphere and outer spheres can have two different radii. If you are measuring distance along a chord between the points, then it is exactly the "classical" version of the problem and the answer is known to be 12. For other values of the outer sphere radii, the question is to my knowledge open, and considered hard. More info here:

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