Pure 22.5 degree angle origami design seems...squirrely...at best and so until I find the time and patience to figure it out, I will stick to other methods. That said, the simple variation shown below is endlessly useful and often works like magic for solving box pleating problems. I first noticed this method in the works of Kota Imai but it seems to be used by a number of different designers throughout the origami community with no distinct starting point. It takes a little bit of intuition to get the hang of, but with practice and patience can be mastered with relative ease.
For examples of this technique in use in a crease pattern, I highly recommend visiting Kota Imai's Flickr page. Many of the models in my gallery also use this design method and I provide an in-depth example on the Box Pleated Design page.