Abelian and non-Abelian numbers via 3D Origami

TL;DR

This paper introduces new 3D origami folding axioms that expand the capabilities of classical origami constructions, enabling the construction of Abelian and non-solvable Galois group numbers.

Contribution

It proposes novel 3D folding axioms involving convex polyhedra to extend origami's arithmetic construction limits beyond traditional axioms.

Findings

Able to construct all Abelian numbers

Constructed numbers with non-solvable Galois groups

Extended origami axioms to 3D folding

Abstract

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.