I was thinking about this projector myself. I am looking at making a short throw projector, so I started thinking about how to replicate this cheaply.
I am not an optics person, so I am not sure if this would work, but this was my idea to test.
I came across these:
Flexible MirrorsI was thinking of cutting thin sheets of particle board and sandwiching them together to form the shape, then use these mirrors stretched over top of it.
I was concerned about the quality of the mirrors, but you can purchase small pieces cheap for testing.
I decided to go a more conventional route and bought a 10mm focal length projection lens off ebay cheap.