Here's another method
(click) which I quite like because you don't have to worry about making slits, which as it says in the link above, should be rounded off/burnished to avoid abrasion of the hinge; that's quite tricky, and so is cutting those slits to register with the hinges applied to the artwork first.
Also the 'slits' should not really just be slits, they should be tiny apertures, IOW it's best if the hinges do not have to be squeezed/forced through them. With this method of cutting an aperture slightly smaller than the paper and then reducing the size of the fall out ever so slightly, you get that result, and you can also burnish the fall out and the aperture it fell out of, which I don't think is mentioned in the link, but if you did that it would effectively reduce the size of the fallout/increase the size of the aperture a fraction anyway.
Wouldn't be much cop for this particular job though as there's not enough room around the artwork (and nor is there for a 'S' hinge really - would have to be a 'U' hinge)!
Just a useful link for reference.