Septic equations are solvable by 2-fold origami

Abstract

In this paper we prove that a generic rational equation of degree $7$ is solvable by 2-fold origami. In particular we show how to septisect an arbitrary angle. This extends the work of Alperin & Lang and Nishimura on 2-fold origami. Furthermore we give exact crease patterns for folding polynomials with Galois groups $A_7$ resp. $PSL_3\mathbb{F}_2$.