Impossible Pentagon

Impossible Pentagon
John Matz
10/11/2020
George Mason University
Math 401: Mathematics Through 3D Printing

This object belongs to the class of optical illusions discovered by Kokichi Sugihara[1], which he calls Reflexively Fused Objects (RFO). RFOs are characterized by their appearance when placed on a horizontal mirror (approximately the position shown in image #1, above) and viewed at a 45 degree angle. Kokichi Sugihara's RFOs appear to be impossible, or at least ambiguous objects, as they are non-symmetric about the x-axis. This is possible due to the difference in viewing angle between the direct view and the mirrored view. These viewpoints are 90 degrees different from each other, so the shape simultaneously presents the two views shown in Image #3. Normally, it should be impossible to create a pentagon in this manner, as it has only one point on the top and two on the bottom, but by manipulating the edges so as to appear different from different viewpoints, the image of a