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 solution by Charlie)

Very good, Charlie!

I knew this was related to "Four Points on a Plane" (pid 2532). Most of the answers to that one involved an equilateral triangle, so explored possiblities involving a tetrahedron or octohedron. 

I see now that I should have payed more attention to the one answer that did not involve an equilateral triangle.

Posted by TomM on 2005-02-14 07:03:37