Start drinking milk! To create this light you will need the plastic from 10 gallons of milk in addition to the DIY lamp standards such as electrical wires, switch, plug, etc.
There are many variations to this polyhedron theme. Dan made a good instructable on the subject. To make mine I modified a simple model I found here which is based on slipping 20 triangles together. By changing the shape to a star of David I avoided having holes in my shade.
A key element to this design is the small color changing LED bulb -- some blend smoothly from one color to the next, however mine was "cheap" ($9 on Canal Street in NYC) and just flips color every few seconds. My kids don't care though, they love it just the way it is..
Step 1: Materials
10 empty gallon sized plastic milk bottles
12 inches green rubber tubing
24 inches rigid electrical wire with a "solid" copper wire inside (as opposed to many thin strands).
Electrical cord with plug attached (preferably cut off some broken appliance)
on/off switch (I chose a button, but you could use a toggle or even a switch on your electrical cord -- if it came off a lamp it might already be there)
Lightweight keyless socket with an edison base (i.e. regular light bulb size)
4" clay flower pot
small plastic container (such as an empty paint sample jar) which fits in the pot
Sticky colored styrofoam from a toy store
green electrical tape
And of course the small color changing LED light bulb
Step 2: Cut and Assemble the Shade
Prepare the milk bottles by cutting them so you have 20 flat, clean pieces. Use goo gone if necessary to remove the sticker gunk.
Print out the template (make sure you print it at 100% size)
Place the plastic over the template and using an exacto knife cut 20 stars. Be careful to hold your plastic so it doesn't slip as you're cutting (alternate: trace the shape with a fine sharpie and cut the star out with scissors). Be as precise as possible.
Assemble 19 stars. It's much easier to do than to explain with words... the pictures will help. The plastic is a little slippery at first, but when more stars are assembled they hold together nicely.
For your last star, use a pencil to trace your socket. You should get the smallest, most lightweight socket you can find so it will fit inside the star. Cut a hole which is SMALLER than the circle you traced so that when you screw in the light bulb it will hold the star in place.
Don't put the last star in -- set it aside for later.
Step 3: Wire the Lamp
Cut your rigid electrical wire in two and push both pieces through the green rubber tube (you can probably find this in a hardware store. I got mine at "Canal Rubber" in NYC). Mark the wires so you know which is which.
Make three holes in you small plastic jar: one for the electric cord coming in, one for the wires going up to the light bulb, and one for the switch.
Make a hole on the side of your clay pot big enough for your electrical cord to go through. You need a masonry bit, but you don't need an electric drill. My little hand drill worked just fine.
Connect the two rigid wires to the socket as indicated in the pictures. Mark the wire that you connect to the white screw (the one which connects to the side part of the socket).
Run your electric wire through the hole in the clay pot, then through your little plastic jar. Connect the neutral wire (the white one, or, if it's not color coded, the ribbed one) to the rigid wire you had marked as neutral. Connect the other rigid wire to the switch. Connect the hot wire from the plug to the switch.
Before going on to the next step, test it now with a standard bulb (not the LED, in case something is wrong...) to make sure you've connected everything correctly... If the light turns on and off, keep on going. If not, unplug it and check all the wires again.
Step 4: Assemble the Lamp
Hold the plastic jar in the center of your pot and secure it in place with plaster. I also put pebbles in to give the pot extra weight. You can use joint compound, but I'd recommend mixing some Plaster of Paris instead: it dries much faster and it's stronger. Keep the jar immobile with a little tape while the plaster cures. Don't worry if you make a mess, it comes off easily.
I did this in two steps, filling the pot up to 1/3 the first time, adding some pebbles, then when it had dried I put extra plaster in to fill it just under the jar's cap. If for some reason there's a bad connection I can always open it up and fix the wiring.
When it's completely dried, put the remaining star on the socket and screw in the color changing LED bulb. Attach the shade to the star.
Step 5: Decorate
Use green electric tape to cover the socket. Not only does this protect the wires from curious fingers, it also secures the shade to the lamp.
I used sticky colored styrofoam to cover the base and simulate weird alien growth... If you've got kids you have probably come across the stuff in toy stores. It's fun and it keeps its shape well, but it gets pretty nasty when it's used around dog hair. On this light it should be good for a while.