The best I could find was 3/4*sqrt(2) or about 1.06066
Call the top face ABCD and the bottom EFGH where the other four edges are AE, BF, CG, and DH.
Mark points at distances of x from A to B, from C to B, from E to H, and from G to H. These four points will always form a rectangle. To make then a square form set the lengths of the sides equal. And solve for x.
sqrt((1-x)^2 + (1-x)^2) = sqrt(x^2 + 1 + x^2)
2 - 4x - 2x^2 = 2x^2 + 1
x = 1/4
Substitute this into either side length to get 3/4*sqrt(2)
I tried many other configuartions for the square, but this is the best I could find.
Posted by Jer
on 2004-12-26 17:48:38