Many of his papercraft polyhedra are illuminated, as you can see in the flickr set I linked to. I decided to replicate and illuminate one of his designs, the "Tri-Star Fruit."
My Papercraft Lantern utilizes surface mount LEDs for illumination, and flexible self-adhesive copper foil as conductors. A single 9V battery provides power, for an estimated run time of about 40 hours.
Step 1: Materials and Tools
Three sheets of 8.5 x 11" card stock (Or get fancy with patterned or textured paper)
Glue (glue stick or white glue)
Copper foil tape (used for stained glass)
Some clear tape (packing tape or Scotch tape)
3 LEDs (I used Digikey p/n 475-2542-1-ND)
A 9V battery clip
One 9V battery
Computer (I assume you've got one of those already!)
A printer (laser is preferable)
A soldering iron
A good, sharp knife with fresh blades (X-acto will work fine)
Wire stripper and other soldering hand tools
Step 2: Print and Cut the Paper
On a cutting mat, carefully cut along all the lines. Obviously, it's important to take your time and get it right. Any blemishes will be very visible, and you want it to look perfect, right? Right.
I found it was easiest to cut from the center outward, then cut the outline last. Again, a very sharp knife is key. If you find it's getting harder to cut a straight line, or the paper edges are starting to fray a bit, it's time to change the blade. Don't throw out the blade, though - it's probably good for other stuff still, just not precision paper cutting.
Anywhere the paper gets folded can be scored. You may use a dull knife, like a butter knife, or you can buy a fancy scoring knife. I use the tip of a pair of scissors. Either way, score along all the fins and along the center folds.
Step 3: Add the Copper Tape
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.
Step 4: Gluing
Using white glue or a glue stick, apply glue to one half of a side without a long trace. Find the mating side, and stick them together. Alignment is critical, so make sure the two pieces are lined up just right. You may find it easier to "flatten" the two pieces while gluing them. Clamp them together with a heavy book for a few minutes, and when dry proceed to glue on the third side. Again, make sure you're only applying glue to the halves without a long trace. It's OK to apply glue to the copper foil, just don't get any on the foil that extends onto the fins (and where the LEDs will eventually be soldered).
Now the battery leads may be soldered on. Decide which trace should be positive, and solder the positive (red) wire of the battery clip onto the very end of the copper foil trace. Mark in pencil if you wish. Then, solder the negative (black) wire onto the opposite copper trace. Be sure not to use excessive heat or the paper will burn. And, don't pile on a huge blob of solder either, or it will remain a visible bump when glued together. Apply a layer of insulating tape over one of the soldered joints (likely the side that's already taped.)
Now, you may glue the final two halves together. This will be trickier to clamp, so be creative. Again, it might be helpful to fold the fins "flat."
Step 5: Soldering
Though the copper tape pieces are facing each other and likely making contact, you may want to add a bit of solder between the joints to make sure they're secure. Paint a minimum of solder onto the gap between the two halves of tape. Remember NOT to bridge the gap between the long pieces of copper that lead to the battery!
Next up are the LEDs. They may be placed anywhere along the fin where there is copper to solder to. If you're using wide-angle (120 degree) LEDs like I used, it won't really matter where they go. But if you're using LEDs with a narrower beam angle then you'll want to consider where the best placement will be.
Remember when you picked one of the long traces to be positive? Remember which one it was? Good. If not, measure with a multimeter until you find it. Take an LED, and solder its anode onto the end of that positive trace, and its cathode to the adjacent trace.
Continue in this pattern, soldering cathode to anode to form a series chain of LEDs. The LEDs may not sit flat on the fins due to the bend in the middle. That's OK, as long as the solder joint is good.
If you have a multimeter, take a moment to verify your solder joints, checking for continuity, shorts and opens.Once you're satisfied with your work, plug in the battery! Disconnect immediately if any of the LEDs don't light, and re-check your work.
Step 6: Image Gallery and Possible Mods
Try using textured or coloured paper instead of white card stock.
And it's very true that you could choose whatever colour LEDs you want. In this design, you could use a red, green and blue LED for interesting colour mixing effects. Or, use a slow-change RGB LED that automatically fades between colours.
You could even go all-out and add light or sound sensors, to make the lantern reactive to its environment.
As far as power is concerned, the circuit could be modified to run on a higher voltage (say, 12V) by adding a resistor to the series chain. Lower voltage operation (down to 3V) is also possible, but you'll need to figure out how to wire the LEDs in parallel instead of series. A Joule Thief might be able to run all three LEDs from a single AA battery...
Best of luck, and I look forward to seeing what you all come up with!