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The radius of a sphere with antipodes 8 cm apart is 4 cm. The distance between the antipodes of a sphere is the diameter of the sphere. The radius is half the length of the diameter.

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How big is a sphere with 6 surface points all 1 cm apart?

A sphere with radius 4/pi = 0.6366 cm will fit the bill - after a fashion. Four points, equidistant on the equator, along with a point at each pole. Of the 15 possible pairs, all will be 1 cm apart along the great circle apart from the 3 pairs of diametrically opposite points, which will be 2 cm apart. There is no way in which 6 points can be marked on any sphere so that each of the 15 pairs is the same distance apart.


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