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 Eight Points (Posted on 2008-02-01)
Eight points are placed on the surface of a sphere with a radius of 1. The shortest distance between any two points is greater than 1.2. How can the points be arranged?

Hint: They are not arranged as a cube. The cube would have an edge length of only 2/sqrt(3) = 1.1547.

 See The Solution Submitted by Brian Smith Rating: 4.4000 (5 votes)

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 re(5): Further improvement | Comment 14 of 28 |
(In reply to re(4): Further improvement by Charlie)

BTW, when the square's opposite corners are pulled in, and the squares bent along that diagonal to make new triangles, you'd probably come up with a snub disphenoid, described in Mathworld and Wikipedia. I don't know if that's inscribable within a sphere without making the triangles non-equilateral.
 Posted by Charlie on 2008-02-02 12:28:56

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