The Huzita-Hatori Axioms:

1. Given two lines L1 and L2, a line can be folded placing L1 onto L2.
2. Given two points P1 and P2, a line can be folded placing P1 onto P2. Line equation is F(s) = P1 + s(P2 - P1).
3. Given two points P1 and P2, a line can be folded passing through both P1 and P2.
4. Given a point P and a line L, a line can be folded passing through P and perpendicular to L.
5. Given two points P1 and P2 and a line L, a line can be folded placing P1 onto L and passing through P2.
6. Give two points P1 and P2 and two lines L1 and L2, a line can be folded placing P1 onto L1 and placing P2 onto L2.
7. Given a point P and two lines L1 and L2, a line can be folded placing P onto L1 and perpendicular to L2.

These rules are also known as the Huzita-Justin Axioms, named for Humiaki Huzita and Jacques Justin, and Humiaki Huzita and Koshiro Hatori respectively. They are a set of rules related to the mathematical principles of origami.

Apparently, because these axioms have several solutions, the resulting geometries are stronger than those resulting from compass and straightedge geometries.