Here is an interesting way to fold a piece of paper quite unlike your normal fold. Like other ways to fold a piece of paper, this one lies flat has many layers and is smaller than the original piece of paper. It is different than a regular fold because of the way the paper twists as it folds. The movement is simple, but very interesting. This type of fold can create some beautiful patterns in origami. Here is a simple version that I read about in Thomas Hull's book.
- Score the folds as marked Dashed lines are valley folds and dot-dashed lines are mountain folds. To experiment, you might want to simply fold the paper into fourths both horizontally and vertically and then create the diamond in the middle. If you would like to create a neater model, score fold lines.
- Collapse the model either along all fold lines at once or progressively.
- H. A. Verrill has some examples of tessellations you can make using the square twist.
- An animation of the square twist is on Wolfram's site (Wolfram Research is the maker of Mathematica software.)