I’ve been learning some interesting things about laser cutting 2D materials to form 3D objects (thanks to the laser cutter I have on loan from Epilog).There are some traditional woodworking joinery concepts that apply, but since all of your cuts are made on a single plane, there are some that don’t (such as dovetailed corners). Inspired by Raphael Abrams’ cigar box Arduino lab, I’m designing a mobile prototyping kit. To make the box sturdy, I’ve designed a pattern of intersections to lock the sides and bottom together, as seen here. The thickness of my birch plywood is 3/16″, so I’ve made 3/16″ grooves on the edges for a clean fit.
My good friend Tod Kurt had done a lot of experimentation in this area, which you can read about in his slides for a Sketching Conference talk entitled From 2D -> 3D.