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Impossible Objects
Look at this picture, called the Devil's Pitchfork. How many prongs does it have?
At first glance it may seem like there is nothing wrong with this picture. However, if you look at the left side of the picture, it appears that there are three prongs, whereas if you look at the right side of the picture it looks like there are only two. If you cover up half the image, the other half will look just fine. In fact, the difficulty arises because of the way the edges are being interpreted as 3d objects.
If you follow the middle prong from left to right, at some point it will cease to be a solid 3d object, and will instead become a square gap. We tend to see 2d pictures like this as representations of 3d objects. But this particular 2d picture represents a 3d object that cannot possibly exist.