A Tessellation from a Square Twist Fold
This Demonstration models an origami fold called a square twist. The square twist folds flat rigidly (the paper is always flat as it folds). It can tessellate the plane and still fold flat rigidly.
"Size" is the number of square twists repeated in each direction. "Dihedral angle" is the angle formed by a specific crease in the square twist. It ranges from to and determines all of the other crease angles. At zero, the square twist folds "through" itself, then repeats the same folding process to unfold in the other direction. The snapshots show the original crease pattern, folding up to the completely folded form at dihedral angle 0, in several different sizes.