If you have a router and the means to cut a straight line with it, this trick for building a 5-sided acrylic box is considerably easier than the common slab-joint method, and gives better-looking results, to boot.
This is not optional, but essential--both for safety and for consistency of cutting depth, especially with thinner material like the 3/32" sheet I'm using here.
Select a 1" (nominal) board at least as long as your panel's longest edge, and at least as wide as Z.
Mount a narrow "heel" of scrap acrylic, or other suitable material, of the same thickness as your workpiece, to one end of the board, as shown. Use short flat-head wood screws countersunk flush with, or below, the surface.
In use, the "heel" will slide behind the workpiece, pushing it into the blade, while the board rides on top of it, holding it flat against the table.
Determine the correct feed direction for the cut. You want the rotating bit to be pushing the incoming acrylic against the fence, as it cuts, rather than away from it.
Remove the cold sheet of acrylic from the freezer.
Put on goggles, ear protection, and gloves. Start the router.
Position one edge of the acrylic sheet against the fence, and hook the trailing edge of the sheet with the "heel" on your push stick.
With your dominant hand, press down on the push stick to hold the acrylic against the router table. With your free hand, maintain gentle pressure against the outside edge of the acrylic to keep it tight against the fence.
With a continuous, steady, relaxed motion, feed the workpiece through the spinning router bit, making the cut.
Repeat the preceding three steps for the three remaining edges of the panel. When you're finished, turn off and unplug the router.
Lay the cut acrylic on top of your work surface with the grooved side down.
Apply a continuous strip of tape along the entire length of each groove, centered, as best as possible, directly over each groove.
Smooth the tape down starting in the middle, on the groove, and working out to the sides and ends. A big advantage of using clear tape, here, is that it's easy to see any spots that are not well adhered.
Cut the ends of the tape strips even with the edges of the acrylic sheet.
Remove the four square pieces of scrap from the corners of the panel. Be careful not to damage the tape as you do so.
Make a single cut in each corner, to free the L-shaped sections of tape that formerly held the square scraps. Cut the "overlapped" side of the "L", and leave the other side uncut to wrap around the corner of the box.
Fold up the sides of the box, as shown. Hold each corner firmly together and wrap the loose tape tightly across the edge. It is vital to get a good seal all the way along the point of each edge.
Stretch a large rubber band around the box, as close to the open side as possible, to help hold the miters together during the gluing operation.
Load a small paintbrush with acrylic solvent cement, and lightly touch it to the top of each of the four vertical joints. You should be able to see the solvent "flash" down the joint from capillary action.
Repeat the above, touching the paintbrush to the center, and perhaps a couple of additional points, along the inside of each horizontal joint. Again, you should be able to see the solvent flowing along the joint.
Let the adhesive sit for several hours at least. Overnight is best.
When the solvent is completely evaporated, peel off the tape.
If you applied enough adhesive, and had good seals at each taped joint, you should now have a sturdy box with nice clean joints and no marring from leaked solvent.
Goo-Gone or generic citrus oil cleaner has proven effective, for me, in removing any tape residue that persists on the acrylic.
Adequate cooling of the cut is essential; a groove that gets too hot will have a bad finish and make a bad joint. The freezer trick I used here might work for you, but longer and/or deeper grooves may require spot cooling at the router bit itself. A vortex tube would be perfect, if you have one, but canned air might be an inexpensive substitute for small jobs.
I am descended from 5,000 generations of tool-using primates. Also, I went to college and stuff. I am a long-time contributor to MAKE magazine and makezine.com. My work has also appeared in ReadyMade, c't – Magazin für Computertechnik, and The Wall Street Journal.