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Impossible Penrose Triangle: Now Possible With 3-D Printing? [Updated]

Ulrich Schwanitz claims to have created a 3-D Penrose triangle without resorting to the usual optical illusions. We'll believe it when we see it.

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 Netherlands-based designer who has tapped a rapid prototyping service to produce what he claims to bea bona fide 3-D 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 left-most edge, but in fact looks like it is below. You can't realize that shape in 3-D without resorting to some sort of optical illusion.

The object — which stands just 5 inches tall — is made from a metallic-like plastic using the Dutch 3-D printing company Shapeways, and to judge by the images, it appears to meet on all three sides at three right angles for a full-blown, stump-the-chump mind screw. The triangle is available on Shapeways's marketplace for $69.95.


Now, normally, when people say they've designed a 3-D Penrose triangle, all they're really saying is that it looks, from some perspectives, like the 2-D 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 three-dimensional 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 3-D 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 not-so-impossible 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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