If I had a photo I would post it for yo uto see.
Maybe I can describe it.... The 2 larger sides of the pieces go together, inverted, one on top of the other (with a glass disk with gold in between). The thin points go on teh bottom and top respectively. Think of it as having a long thin balloon, twisting it at the middle, and pulling each side out. Then put it on a small square base, and put a lamp shade on top, lol.
Thats what it should look like.
I think your idea of having them as hanging lamps is excellent.
If you keep them you should try it out!