Step 1: What you need
Below is the shape as an image, and i've also attached a DXF file.
You will need sheets of paper or plastic that allow light to get through. The stiffness of your material determines how large your pieces can be - stiffer material for larger pieces and larger lamps, thinner material for smaller pieces and smaller lamps. (see next step)
You will need a lamp fixture - just a raw socket on a cord. I found some nice ones at Ikea for $4, and some fluorescent bulbs. Use a compact fluorescent bulb so you can get more light without melting the plastic.
I experimented with a number of different plastics and sizes for the parts, here are my results:
- HDPE: works well, looks good, cheap and easy to get. I used 0.8mm thick stock for 8cm pieces (measured flat-side to flat-side). That's about the smallest you'd want to go with that thickness, you could go up to 12 or 15cm with that thickness. this is the least expensive plastic by far. One of the commenters suggested using plastic milk-bottles, which are made of HDPE, this is a good idea!
- Acetal (delrin): this seems to be the best choice for looks, it has the purest white color and best light dispersion (basically, looks just like acrylic except it doesn't crack as easily). I used 0.35mm stock for 6cm and 8cm pieces, and 0.5mm stock for 8-12cm pieces, and 0.65mm stock for 12-15cm pieces. It still is a little brittle and harder to work with than HDPE, and more expensive. if you cut this with scissors it will be somewhat tricky due to the brittleness, but possible.
- Vinyl: I did not try it, probably want to use thicker pieces since it is not very stiff. but you can use colors!
- Paper: I did not try paper but it should be good for smaller constructions.
- Laminated paper: this is a great idea suggested in the coments section. try laminating color tissue paper, then cut the pieces from that. very unique and colorful!
- Acrylic: too brittle, it will crack when you try to assemble. too bad!
- Nylon: has a yellow-ish look when lit up which makes it undesirable.
- for a large construction use stiffer material for the same size piece. ie, if you are making a lampshade with 12 pieces use thinner material than if you are making a shade with 100 pieces, assuming same size pieces.
Where to get it:
HDPE 1/32" sheet: sheet: http://www.usplastics.com item number 42584
Acetal sheet, 0.015" and 0.020":: http://www.mcmaster.com item number 8738K52 and 8738K53