Quote:
Originally Posted by Daithi
If you roll it up you have three sides. Two ends and a center (picture a rolled up rug), but I look forward to seeing your answer pdurrant.  |
Ah! I see. OK, that's a pretty good answer. The edge between the 'sides' isn't really like the edge of a piece of paper, but it could be argued that my solution is flawed too, so I think I shall declare a winner.
My solution is the trihexaflexagon.
No, it's not as bad as it sounds, really. Here's how you make it. Take a strip of paper that's at least 6.5 times longer than it is wide.
Now fold it up in equilateral triangles. You want to end up with ten triangles.
Now fold the strip into a hexagon. One triangle sticks out (the tenth), along with any bits of extra paper.
You can fold and stick the extra bits of paper past the first and last triangles onto the first and last triangles, or just cut them off. Then stick the first and last triangles together.
Now you have your trihexaflexagon. Fold both ways across all three corner-to-corner lines. Now fold from the centre into valley/mountain/valley/mountain/valley/mountain.
There are two ways to do this. One way is dull. The other way: as you push in the valleys to make to mountain folds as sharp as possible, the centre opens up, and you get back to your hexagon. And you can keep doing this. fold open, open from centre, fold up, open from centre.
And where do the three sides come in. Well, if we colour the two sides of the hexagon of paper, say red and blue, and then do the folding/opening from the centre, we find another side that we haven't coloured yet. It will go red/white/blue/red/white/blue!
But you really need a video to see it working. Or make one yourself!
Here's a video (not me!):