This is my favorite shape. It's called a Penrose Triangle, and it's something known as an "impossible object." It can be drawn on paper, but it cannot be constructed in real life. I find this concept to be very interesting, as I find not only shapes which meet this criteria, but ideologies as well.-Bret AlanWikipedia: Penrose triangle And, while you can't create an actual 3-D Penrose Triangle sculpture, you can create one which gives the optical illusion of one: Creative Commons
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.