  In this work we introduce new folding axioms involving easy 3D manoeuvres
with the aim to push forward the arithmetic limits of the Huzita-Justin axioms.
Those 3D axioms involve the use of a flat surface and the rigidity property of
convex polyhedra. Using those folding moves, we show that we can construct all
Abelian numbers, and numbers whose Galois group is not solvable.
