Microsoft handed those (well, not the 'double' one) out a couple of years ago as Silverlight/Expression swag, pretty sweet toy and fun to play with.

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.

Buy one ($65!):

http://www.momastore.org/museum/moma/ProductDisplay?catalogI...

The build quality on this one is not as high as I had anticipated (considering the cost). Though it is still good for blowing a mind now and again.

ha! I just googled for it after I saw it, same link. However cool it might be, I'm not paying 65$ + s&h for it!

I feel the same way about a Gomboc (self righting shape) http://www.gomboc-shop.com/

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.

But at least there is a reasonable reason for the Gomboc's high price: the exacting tolerances on the shape.

I remember getting a Taco Bell Star Wars toy just like this when the special edition came out.

http://www.listia.com/auction/20297

It does the infinite folding thing but doesn't split into two stars.

reminds me of disassembling a sphere and reassembling into two spheres. damn topologists.

You're thinking of the Banach-Tarski Theorem, sometimes called a paradox. Mentioned here several times.

http://searchyc.com/banach+tarski

Same connection was made last time: http://news.ycombinator.com/item?id=416765

The actual article (linked and quoted in the BoingBoing one) goes into the connection in much more depth, pulling quantum mechanics and the Big Bang into the mix:

http://forgetomori.com/2009/science/folding-the-yoshimoto-cu...

Interesting. When I get back to a fast connection I'll track that down. Thanks.

Make one yourself from colored paper. Video showing how it's done at http://www.metacafe.com/watch/1014711/crazy_star_cube_nice_p...

Oh, and this is a simpler variant, but interesting nevertheless... http://www.metacafe.com/watch/783529/unbelievable_white_or_b...

I made one out of wooden cubes and two colors of duct tape.

Can you post a how-to? This would make a pretty great present.

Should mention that I wasn't extremely happy with the result, although it's still kinda neat. The fibers in the tape kind of hang off the edge (perhaps a sharper knife would help with that), and the whole thing is rather sticky, since the edges start peeling up a little. Perhaps something like gaffer's tape would work better.

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.

Some discussion from a year ago, and a link to another video.

http://news.ycombinator.com/item?id=416514