Appears in collection : Geometry in non-positive curvature and Kähler groups

Start with a pentagon in the euclidean plane, and consider the space of all pentagons with the same side lengths up to euclidean motion. This space is the real part of some K3 surface. Folding the pentagons along their diagonals, one obtains involutive automorphism of this K3 surface. I will describe the main dynamical properties of the group generated by these involutions. This is based on a joint work with Romain Dujardin.