Paper is an amazing thing. In Japanese culture, for centuries, walls and furnishings were made from timber and Washi (hand-made Kozo fibre paper). Candle-driven laps made of paper (counter-intuitively) are still common, this is an Andon Lamp:

There are 2 versions of this – one that uses 4 squares (this one) and another minor variation makes the frame with 4 bits of paper and then you put in other paper inserts into frames formed on each side of a contrasting colour/texture.

Made to be lit from within, I was going to demonstrate that but cannot find my cache of tealights for now.

I like this, small scale it is charming, larger scale you can vary the proportions to make it more upright, elongated or indeed change the number of facets. the locking mechanism is ok, but if you were making it for actual use I think you would need to reinforce the joints with glue.