A quick web search reveals thousands of images of laser-cut living hinges made of wood. Examples in acrylic are not so common. It took me a bit of experimenting, but I was finally able to find the exact ratio of cuts to material thickness suitable for eighth-inch acrylic. Except for the clasp (more on that below), these boxes are actually just two pieces of plastic. The "covers" are formed from a piece with a single 180 degree bend and the "edges" are formed from a single piece with two 90 degree bends.
I fashioned the clasp to hide an embedded spring. This allows the boxes to latch securely. Gently pulling the clasp back against the spring will allow the box to open.
Clearly, these are not the most durable pieces and wouldn't stand up to regular use in a purse or backpack. But they are quite lovely for storing special treasures. They measure about 4 x 3 x 1 inches.
Later, I made some more with different designs: