On 10/10/07, David Gale <gale@math.berkeley.edu> wrote:
... It surprised me until I found an origami example on the internet. There's whole lot of stuff on this problem, e.g. http://www.ics.uci.edu/~eppstein/junkyard/teabag.html
One of the most detailed accounts near the end of this page, signed Narasimham G.L., mysteriously peters out in the middle (quite literally!). But it seems from that and other contributions that the optimal solution does not actually have the symmetry of the square --- which I find highly counter-intuitive. Another point that nobody seemed to pick up about the early attempts at solution (such as my casually suggested 1/8 cube) is that any flat flap results in an immersion rather than a proper embedding; but that carp was in any case overtaken by later events. Fascinating material about a beautiful problem! WFL