A lamp I made in the shape of the 34th Stellation of an Icosahedron. This is actually the same shape as my "Star". You might find more of the idea of the geometry of this lamp by looking at the "Star".
The skeleton is made of metal rods I soldered together. To that I glued rice paper. And of course inside is a light. I made one "spike" removable so that the light bulb can be changed in the future.
The underlying model I built using the instructions I tried to spell out under my "Star" model.
Once the cardboard model was built I cut the copper rods. I attached a scan of my notes for the rods. Their lengths are exact relative to each other, but their final lengths depend on how large of a lamp you want to build. Another scan gives you more of an idea of what that final length might be.