Step 5: Other Ideas
the lampshade shown below i spotted hanging from the eaves of a hotel in china. it is made from i think 6 identical pieces (possibly 7 or 8). each piece is a large diamond shape with slots cut in it to allow sliding the pieces together. it looks like each diamond is slid into itself to form one of the central vertical tubes, its free tips are then slid into the other pieces to hold the whole thing together. (i have not actually made one yet, so please comment if you have).
you can also usually find one or two polygon-inspired lampshade designs at your local designer lighting store, and at Ikea.