Co.Design
Impossible Penrose Triangle: Now Possible With 3D Printing? [Updated]
The solution has been revealed! Read more about it here, and check out the video below. —Eds
Science tells us the object you see here cannot exist in the real world. It's an illusion. An Escherian ruse. Ulrich Schwanitz says, "Pfft."
Schwanitz is a Netherlandsbased designer who has tapped a rapid prototyping service to produce what he claims to bea bona fide 3D Penrose triangle. Mathematically, that's impossible: The trick of a Penrose triangle is that each joint appears to be connected at a right angle — meaning that the bottom right edge of the triangle should connect above the leftmost edge, but in fact looks like it is below. You can't realize that shape in 3D without resorting to some sort of optical illusion.
The object — which stands just 5 inches tall — is made from a metalliclike plastic using the Dutch 3D printing company Shapeways, and to judge by the images, it appears to meet on all three sides at three right angles for a fullblown, stumpthechump mind screw. The triangle is available on Shapeways's marketplace for $69.95.
Now, normally, when people say they've designed a 3D Penrose triangle, all they're really saying is that it looks, from some perspectives, like the 2D representation of the triangle. So an object that seems like a closed triangle from one view will reveal itself as a skewed horseshoe from another. Or a triangle that's in fact closed on all three sides will feature warps in the beams that are invisible from certain vantage points, making the whole thing appear as though it has three right angles.
Schwanitz insists he has not resorted to the usual trickery. "We have taken a new approach at bringing the impossible Penrose triangle into the real world,? he tells us through a Shapeways press rep, "and have designed a truly threedimensional object which, unlike other attempts to create a Penrose triangle, this model does not have any hidden openings nor hidden twists."
That doesn't eliminate the possibility of some other visual trick. Schwanitz refuses to share a 3D model of the triangle online (as is SOP on Shapeways) and has given the media just two images of the object — both from the same perspective. These two facts suggest that Schwanitz's "impossible triangle" comes from the same family of optical illusions as the other notsoimpossible Penrose triangles. As for specifics: Schwanitz declines to divulge his secret. "We would rather like people to scratch their heads a little longer," he says.
[Images courtesy of Shapeways]
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It's only impossible if the objects are cubes that meet at right angles. If they were proper cubes, the design above wouldn't be 3d printable, because there would be gaps between them.

Oh, you mean the "false DMCA takedown notice" poster?

Well done!.
I made one too: I made a rotating version by changing the orthogonal angles:
http://www.youtube.com/watch?v... 
I think I got it. Everything is plain simple as all genius. Our eyes are tricked by other well known illusion:
These cubes are not convex but concave! They only have three back sides but our mind thinks these are front. That explains why the top side is darker — this is the shadow.
Check out the detailed illustration at: http://flickr.com/gp/zkeeper/2...
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