A tour of the axioms

Note

This tour is a work in progress. See the Specification for the complete axiom reference.

The Huzita–Justin axioms are seven operations that define all single-crease folds achievable on a flat sheet. Beloch exposes each as a built-in operation.

Axiom 1 — line through two points

Given two points, there is a unique line passing through both.

paper square
through .a .c
through .b .d

; status: works — both diagonals of the square
paper square
through .a .c
through .b .d

axiom 1

through P Q draws the crease line through points P and Q. No fold is applied — this is a crease-only operation.

The remaining axioms (2–7) will be documented here as they are implemented. Axiom 2 appears implicitly in @map (the fold that places one point onto another).