This is a very basic overview of how to make this lamp, inspired by this red one: https://www.instructables.com/id/Universal-lamp-shade-polygon-building-kit/step5/Other-Ideas/
It was a learning experience, and I can tell that some of my choices weren't ideal. However I never got around to coming up with something better, so here you are. Also I made this 2 years ago, it might be a little vague, sorry.
Step 1: Materials
What you need:
-Persistence and creativity to actually get this to work out how you like.
-Some electrical knowledge, or someone who has that, or some sort of kit, or an existing lamp.
-A large, bendable, translucent material that wont melt or burn. I used mylar that I found at the book store near the art campus. I bought it by the foot, and you'll need to figure out how much you need by planning out how you can cut out the pieces.
-Two-way tape or something equivalent.
-Wire - a coat hanger could work
-a socket, light bulb, cord, switch, and chain, soddering tools
Step 2: Making the Lamp
I cut the mylar into 8 diamonds, each 14 inches tall, with 60 degree angles (like two equilateral triangles).
Then add slits like in the picture. Each slit ends in the very middle of the shape.**Edit. I found my page of scribbles and these are the measurements I used. **
Attach the pieces. Each top slit goes into a bottom slit. The second picture is an idea of what it will look at from the top. This is just three pieces, and you can see where the slits line up (in red). The first cross creates a cylinder, and the next two add decoration and stability.
Do step one on each piece, then step two to connect them, and step 3 to finish. At some point you connect the chain into a circle, with the pointy flaps on the outside.
In addition, I think I used double stick tape between each cylinder. I'm sure this depends on the material etc.
Step 3: Electrical
You will need a light inside obviously. My dad helped me on this part a bit.
Get wire with a plug, and chain, and feed the chain on. Then put on a washer -this should be decently big, and this is how the shade part will be attached. Then sodder the wire to the socket, and screw in the bulb. CFLs don't get very hot, so go with one of those.
Add a switch to the wire. We bought this at a lighting store, and it was pretty easy to add, anyone can do it, no tools involved.
Step 4: Assembly
Now to bring the electrical and artistic together. Take some wire and bend it into a circle so it fits snugly inside the shade. Cut three pieces of wire exactly the same length ( so it will hang evenly). Use these to attach the wire circle to the washer.
Then, tape the wire to the inside of the shade, maybe about 1/3 down. The whole thing is fairly light, which is why tape and flimsy wires are okay.
At this point, try hanging it up. You might notice that the bottom collapses in and loses its shape some. To fix this, I took a wide strip of clear plastic (extra lamination), rolled it into a circle and put it up inside (in the middle/bottom). I didn't even tape it into a circle, and that way it puts a springy pressure outward, keeping a cylinder space open in the middle.
An alternative: form another circle of wire, and tape that in 1/3 of the way up from the bottom, or use wire to suspend it from the other circle.
Stand back and admire!!
Step 5: Notes - What I Learned
The mylar I used was not stiff enough. It would keep its shape better with something more sturdy. Also it can get creases and marks in it if you are not careful. On the other hand, gentle bumps are fine, the lamp just squishes a little.
Tape makes it look clear, probably applicable for any frosted surface. So use small pieces and make them tidy.
How far apart the slits are is critical. Make sure to make a design out of paper that you are happy with ahead of time. In fact, feel free to try more or less pieces, a different angle of diamond, or even an oval - that could be cool! This should be whatever you want it to be.
You might want someone to help you assemble it. Extra hands are helpful.
Feel free to ask me questions. I know that this is really just a sketch, there are probably some gaps and definitely details missing. So feel free to ask questions, and I will answer to the best of my ability. But also, it depends a lot on what you have on hand. I think every step could be substituted if necessary. Sorry I can't give you a great instructable!