Texture Editor job. My goal was to unfold the mesh with as few cuts as possible. As you can see, the frog in the T.E. now looks like he's been squashed under a truck! :)

However, this method was a mistake. Keeping all the polygons attached to each other makes you distort those polygons. At the end, the polygons in the T.E. were so deformed that the texture looked too much stretched on several faces.
I had to modify the organization of the UV's.