I have a great idea for a geometric lampshade that I would like to build. Think of something roughly resembling a geodesic dome. It will be made of individual triangular panels of roughly the following shape, each of which will be made of wood, with rice paper stretched across it.
My question is about how to fasten the frames together. The frames will be made of strips of wood with a cross section of about 3mm by 15mm, which need to be attached together face-to-face, like this:
They can't be glued because I want to be able to take it apart again if the rice paper needs replacing.
The tricky thing is that the fastener needs to have a flat profile. If I were to drill a hole through them and use a bolt, the nut and the bolt head would cast a shadow on the rice paper. So I'm looking for a way to fasten them that will have a fairly flat profile and cast as little of a shadow as possible.
(It's kind of hard to describe how this thing will fit together, but in the above (yellow) picture the light is shining down from the top, rather than from the side, and the rice paper is at the bottom.)
So, tl;dr, I'm looking for a reversible way to fasten two strips of wood about 3mm thick, such that the fastener sticks out as little as possible from the finished piece.
It doesn't need to be super strong because it's only for a fancy lampshade, but it would be great if each fastener is easy to install, because the thing will be nearly a complete sphere and the fasteners will be on the inside, so the last few will need to be done by reaching inside it.
In case it's relevant I have only very basic woodworking skills and no fancy tools, but I can use 3D printed jigs to make cuts or drill holes in the wood with reasonable accuracy. If I don't need to make holes in the wood then it will save me some work.