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.

(In reply to re(3): Further improvement by FrankM)

Interesting that Dej Mar saw a tetrahedron pair, while Bractal & brianjn jumping off point was the (nominally suggested) cube.

I can't help feeling amusement at the fact that the irony of this statement passed without comment. (Turn away if you wish to reconsider it).

Of course, "tetragon pairs" is just another name for cube. 

Posted by FrankM on 2008-02-03 21:46:00