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.

If you take a tetrahedra where one vertex was at the "north pole" of the sphere, and the three other vertices were placed equidistant from each other and the pole and 15 degrees above the "equator".  Then take a second tetrahedra, indentical to the first but inverted so that one vertex was at the "south pole" of the sphere and the second tetrahedra was then rotated 180 degrees so that, if one took a polar view of the two tetrahedra base-lines, they would see a star of david.  

 

Edited on February 1, 2008, 11:04 pm

Posted by Dej Mar on 2008-02-01 13:10:59