An Algorithm for Finding the Veech Group of an Origami

Abstract

We study the Veech group of an origami, i.e., of a translation surface, tessellated by parallelograms. We show that it is isomorphic to the image of a certain subgroup of Aut+(F 2) in SL2(Z) ≅ Out+(F 2). Based on this, we present an algorithm that determines the Veech group.