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.

Can anything be done with tetrahedrons? For example how about two tetrahedrons in tandem with each other? (Sort of like a 3-space model of a tetrahedral prism for 4 dimensions) Putting their points apart equal to side length would assure that 5 out of 7 lengths were equivalent.

A hexagon type format for six of the points wouldn't work, as you would have the 30/60/90 triangle.

Posted by Gamer on 2005-02-13 20:58:46