The geometry of a fold.
One line.
A fold is a rotation about a straight line. Nothing stretches and nothing tears. Whatever was on the reverse of the paper now faces you.
Four lines meet.
Where creases meet at a point, they move together. This one closes completely only if alternating angles add up to 180°. That rule is Kawasaki's theorem. Move one crease and try it.
- Alternating angles
- When folding stops
- Fold directions
One motion.
Repeat that vertex across the sheet and every crease shares one motion. A single number sets all of them, and the sheet shrinks in both directions at once.
- Width
- Length
- Footprint
Pull one corner.
Koryo Miura designed this pattern so one pull could open a whole sheet. A solar array folded this way flew on Japan's Space Flyer Unit, launched in 1995. Drag the corner, or use the slider.
- Footprint
Your sheet.
Set the pattern, then print it. The file is a real crease pattern at A4 size. Score the lines, fold along them and pull one corner.
