Arrange 8 points in 3-space so that for each of the 56 triples of points that they determine, at least two of the three distances between points in the triple are equal.

(In reply to First thoughts. by TomM)

Another thoght I had was to take two tetrahedra and "interlace them. (Sort of the 3-D version of the Star of David) It wasn't until I started working out the distances that I realized that the eight vertices of such a figure form a cube.

Posted by TomM on 2005-02-14 00:39:20