In my talk I will be considering branched covers of complex tori. It turns out that the space of genus 2 covers of the square torus $mathbb{C}/mathbb{Z}[i]$ admits a natural geometry in which it is tiled by squares. I will describe this geometry in detail and use it to classify $mathrm{SL}(2,mathbb{Z})$ orbits of square-tiled surfaces in genus 2.