#7: One-Cut Crane / イットウギリヅル
#8: One-Cut Hole Crane / イットウギリアナヅル

The one-cut crane has an interesting story. Once upon a time, the paper of life was folded just so, that when the sword of division attacked with one swing, a beautiful crane came out of it.

The one-cut hole crane is the hole left behind. A reminder of the miracle that formed the one-cut crane.

This crane is based on the fold-and-one-cut problem, where you fold a piece of paper such that when you cut it with one straight line at a certain angle, it gives you the shape you want. This problem has been solved with two different algorithms: a straight skeleton algorithm (which is more practical and works almost all the time, except that it can create dense creases), and a disk packing algorithm (which works always, but is less practial). I used the straight skeleton algorithm for this. Thankfully, there aren’t any middle flaps, as those can get tricky to deal with.1

The cranes were folded by printing the crease pattern, taping it to some origami paper, creasing the creases, and then separating the origami paper and collapsing. Afterwards, I cut at the appropriate position and angle.

  1. I once tried to fold-and-cut a whole message (only a few words), and the word in the middle (I think it was “BIRTHDAY”. It was a while ago.) was so full of middle flaps that I gave up and just cut each letter individually. Middle flaps are such strong enemies. ↩