Step 1: Materials
3mm Baltic Birch plywood
1/4" square wood strips
Power chop saw with 60-80 tooth carbide blade
Thin blade razor saw like X-Acto extra fine razor saw
Low tack masking tape like 3M blue tape
Wood glue like Titebond II
stain or paint
Figure out your outside dimensions. Be sure to add the width of a saw cut to the height if you will be sawing off the top to make a lid. Cutting the lid after gluing the box makes everything line up great.
Step 2: Cutting Pieces
The key to this method is to cut the pieces a little large then use a stop block on the chop saw to get the pieces exactly the right size.
1. Cut the pieces oversized but nice and square. I ripped them on my table saw then sliced them up on the chop saw. Use a really good blade for minimum chipout. Hold each piece tight to the fence and tight to the stop blocks so your cuts are true.
2. Follow the cut diagram in the second photo and make Cut 1 as a 45 degree bevel cut. It is on the oversized stock so just make sure you aren't cutting off too much and cut it as shown in the third photo. All of the pieces get a Cut 1. Keep your fingers out of the way.
3. Cut 2 is also unmeasured. It is at right angles to Cut 1. All of the pieces get a Cut 2.
4. Cut 3 is the first measured cut. It sets the width of the box and goes through the front, top, and back. Set a stop bock as shown in the fourth and fifth picture with a thick square scrap piece and a strong clamp. This will make all three pieces identical width. Cutting a scrap piece first and measuring it will get you very high accuracy.
5. Cut 4 may be the trickiest. It sets the length (front to back) of the box and goes through the left, top, and right. Set the stop block at the length and test on a scrap piece. Cut the final bevel on the top piece and correct sides of the left and right. Don't feel bad, I messed this one up too until I drew up my cut diagram.
6. Cut 5 sets the height of the box. It is a 90 degree cut so move your chop saw back to 90. It goes through the front, back, left, and right. If you are making a 6 sided box, you need to make two 'top's and cut a 45 degree bevel for Cut 5.
7. The box is pretty strong, but I wanted reinforced corners so cut your 1/4" stock so it will fit inside the box. I just cut them with my X-Acto razor saw. Cutting them on the chop saw will just make the cutoff disappear in a blink. You can use triangle profile reinforcement pieces if people will be looking inside and you need reinforcement.
Step 3: Assembly
2. Flip over the assembly and put glue in all the bevel faces. Use the glue sparingly so it doesn't squirt out all over. I like to use a toothpick or acid brush to spread it.
3. Corner by corner fold up the sides and tape them together. spread glue on the reinforcing pieces and put them in. They stayed in place for me when I gave them a firm press, no tape needed.
4. Let it dry completely. Patience!