I am fairly new to box pleating and tessellated patterns but this one caught my eye and I had to try it:

Oddly, it works on 120 degree angles, so a hexagon is perfect as a starter. I would like to say it was all neat and went to plan, but the individual “triangle twists” are not as even as I would like (I put that down to having no idea what I was doing initially) – certainly they got better the more of them I completed:

I get the impression that the smaller the pleats, the more of the units fit, but the more complex the interaction between them so you get folded into fiddly corners. I quite like the triangle twist method, some pleasing shapes emerge from it.

You should give this a try – do not be frightened by the link, the instructor speaks English amidst the sea of German: star puff