Or, you can do miter-fold joints on your CNC. The basic idea is that you cut almost, but not quite all the way through the material with a large V-bit, cut out the outline of the part, then lay down a bead of glue and fold the joint. The joint can then be held together with tape until dry, and any roughness in the joint is easy to round over with the side of a round screwdriver shaft, or sand away. The joints actually fold very nicely, and they lay down really well.
Aspire and VCarve Pro make it pretty easy to lay out and cut these boxes, using a v-bit designed for this. We're using an Amana 91-degree insert v-bit made for this purpose. The 1 extra degree leaves space for the glue and any stray dust when you fold.
For this project we're using 3/4" MDF core walnut veneered sheets. There are about 36 sheets of material for the project. We're cutting the v-grooves leaving about .005" at the bottom, which seems to leave them sturdy enough so that we can move them from the CNC to the assembly table without breaking them, and still fold nicely. After folding, we're just clamping them with strapping tape.
We're about halfway through making the slats at this point after 3 days of cutting and folding. Here are some pictures. The first is the CNC cutting, the second is boxes on the assembly table awaiting gluing, in front of a couple of wall frames with some partially finished boxes on them, the third is taped-up boxes waiting for the glue to dry and the fourth is a bunch of boxes after sanding
