This evening we finished pulling all the staples out and getting the fabric off. We made sure to make pictures of every little step we made and of things that may come in handy when putting it back together again. Furthermore we labeled every piece so we know what is what. I'm sorry to say that we don't have any pictures of the 'naked' chair, we simply forgot to make them.
Tom did the calculations, and we need approximately six meters of fabric (with the standard Ikea width of 1.50 m). I wonder what we will get at Ikea.