Kokichi Sugihara produced an optical illusion of figure that looks like a circular cylinder when viewed from one angle but like a square cylinder when viewed in a mirror (https://www.youtube.com/watch?v=oWfFco7K9v8). We illustrate this illusion with a curve in 3-space. To see the circle, rotate the space so that the blue and green axes line up (1 with 1, 2 with 2, 3 with 3, and so on). To see the square, rotate the space so that the blue and negative green axes line up (1 with -1, 2 with -2, 3 with -3, and so on).
