Laser Cut Polyhedra
I've been toying around for a while with the idea of laser cutting through the material at an angle to create a mitred edge. Cut enough of these edges and you can still all the shapes together to create special boxes of polyhedra. I finally got round to testing it and it works really well. You can see all the cutting details over on the JustAddSharks blog here, but for now I'm just sharing pictures of the polyhedra I made using this technique.