Yoshimoto Cube
boingboing.net
boingboing.net
You can make a continuous folding 2d variant with paper fairly easily as well, though I don't know for the life of me how it's called.
I'd love to play with one and leave it on my desk as a fidget toy but it's not worth 99 euro to me for just that.
http://www.listia.com/auction/20297
It does the infinite folding thing but doesn't split into two stars.
http://searchyc.com/banach+tarski
Same connection was made last time: http://news.ycombinator.com/item?id=416765
http://forgetomori.com/2009/science/folding-the-yoshimoto-cu...
Not sure I'll get around to posting a full how-to, but the idea is that I took 1 or 1.25" square dowel and cut it into 8 cubes with a hand saw & miter box (table saw with a fence would give more consistent cuts though). Taping involved putting down a piece of tape sticky-side-up, setting down the cubes adjacent to each other, and then cutting off the excess with an x-acto knife.
You should be able to follow a video of one of these to get the joints and proper colors figured out.