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.

I think it is fair to say that the general layout for the eight points is within close proximity of or at the vertrices of a regular square antiprism.

By allowing for all lengths to be of a minimum distance greater than 1.2 with the maximum being barely more than 1.224 (I base that on Charlie's data Lat. 33.7 Sq. side 1.200 Tr. side 1.224) then there are some other arrangements which are possible; I'd hate to be the engineer called in to construct them!!

Posted by brianjn on 2008-02-02 19:58:21