Somehow, I always pictured in my head that it would have to be possible to do a butterfly (pictured below), but it took me forever to come up with the fifth & sixth steps that appear below. When I finally did, I was quite surprised at the final appearance. In particular, the interesting symetrical pattern on the top of the wings came as a pleasant shock.
Fold the bill precisely in half top-to-bottom, then unfold. Fold the bill precisely in half left-to-right, then unfold.
Fold the bill precisely from corner-to-corner diagonally, then unfold. Repeat this fold for the other two diagonal corners.
Fold both ends as shown. This odd angle fold is from the upper corner of the bill to about 1/2 inch inside the lower corner on each side. Try to make the folds symetrical. These folds will remain - do not unfold.
Following the diagonal creases created two steps above, refold and re-unfold along each diagonal. (This is to crease the end folds created in the previous step.)
While the diagonal is held folded, fold and unfold along the "half top-to-bottom" the two corners that have the end points of the diagonal fold. (This is difficult to describe in writing - look at the picture!) After these two creases are complete, open the diagonal fold and repeat this step for the other diagonal fold.
Believe it or not, this picture shows the next fold (singular). Using all the folds/creases created before, simply bring the left & right ends together while "encouraging" the half left-to-right, both diagonals, and the folds made in the previous step to re-fold. If you're doing it right, it will start to look like the picture, but won't quite close. Holding the half left-to-right and both diagonal fold creases closed, gently force the center section of the bill to close. This will create four new folds (automatically in the correct place if you don't let anything poke out the wrong place). If anything extra is sticking out, don't close this fold. Re-open slightly, tuck it back in, and try closing again. (This is quite difficult to describe, but is not hard to do!)
Along the line between where the top/bottom edges intersect the diagonal folds, make a new fold. (Look at the picture.) This will be the narrowest point along the "wing". Do this on both sides of the center, keeping the folds symetrical with each other.
Unfold one of the folds made in the previous step. Parallel to the crease from this fold, fold the "remainder" of the center in half. Do it again. (These folds are tough to get tight since there are so many layers of paper here.) This center portion ends up as a long, skinny "body" for the butterfly.
Open both wings along their folds. The body should look like the image on the left (on one side). Notice that portion of the body along the center folds are slightly larger than along the edges of the bill. Fold the larger portion tightly over the edges. Then twist a small amount of the end over in the same direction. (This is what keeps the body portion from unfolding itself.) It isn't too critical how you do this as long as the body stays folded. (Sorry, this doesn't show up too well on the flatbed.)
Fold the wings down again. You're basically done. You can "pinch" the tips of the wings to get a slight rise and more pointed look. (No way to show on a flatbed - fake it.)
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