3D Realization of Penrose Polygons Using Non-Rectangularity Trick

Abstract

This paper generalizes an impossible figure called a "Penrose triangle" to regular polygonal figures and proposes a method for constructing real 3D objects from such figures. Two well-known tricks, namely the curved surface trick and the discontinuity trick, have been used to construct 3D objects from impossible figures. However, these tricks are very sensitive to viewpoint. The proposed method uses only planar faces and connects them wherever they appear to be connected. The resulting objects are thus less sensitive to viewpoint in the sense that the impression of impossibility does not disappear when the viewpoint slightly changes. Moreover, the constructed objects have the same symmetry as that of the original figures, preserving their elegance.