Step 3: Add the Copper Tape
The LEDs are all mounted on the upper-most "fins" of the lantern. So, that is where the traces must lead. Also, it's important to realize that all the traces meet in the same place - this means that with the proper planning, the LEDs can be arranged in a series configuration that uses a minimum of copper (and, ahem, effort).
Each of the three sides of the lantern will have a different pattern of traces. Start with the side that has just two short strips. As you can see in the photo, the strips should be laid parallel to the middle fold, about 2mm apart, and reaching from the tip of the fin to about a centimeter beyond the fold. Flatten the copper using the handle of a pair of scissors, or some other smooth, rounded object.
Now move on to the next side of the lantern. It will have one short strip, like the first side, and one long strip that goes all the way down to the base (where the battery will eventually connect). Place the short strip first, in the same manner as the first side (about 1-1.5mm from the center fold). As you may have guessed, this strip should line up perfectly with one of the strips laid out on the first side.
Now lay out the long piece. It starts out in an identical manner to the long strip, but continues down the edge of the lantern. Where necessary, fold (but don't cut!) the copper foil to make turns as necessary. With 1/4" wide copper foil tape, you could only have to do four folds to reach the bottom of the lantern.
Flatten the copper foil with scissors.
Now, the third side. It is essentially a mirror image of the second side. Lay out the copper foil in a similar manner to the second side, but the long piece of copper should travel down the opposite side of the paper. Flatten with scissors.
Lay out the three sides of the lantern with the points inward. It should be easy to see how this will work: the three LEDs will align for a series circuit at the top of the lantern, and the matching copper foil traces will connect the circuit between the three sides. But wait! The two long traces will short together! Indeed they will - an insulator is needed between these two traces.
Pick one of the sides with a long trace, an grab a roll of tape. It doesn't really matter what kind - packing tape, Scotch tape, masking tape. Just as long as it isn't conductive. It should be a light colour though, to a void the chance of seeing it through the paper. Lay down a layer of tape along the entire length of the long trace, leaving just a small exposed section at the base where the battery wire will be soldered to (that will be insulated later.) Make sure the tape covers to about 2mm beyond the fold at the top fin, so it doesn't short together at the top. If any tape is hanging over the edge of the paper, trim it off with a knife or scissors.
As with the copper foil, flatten the tape with scissors to remove any air bubbles.