Challenges in Plane Symmetry: From Theory to Perception

The planar ornaments are created by repeating a base unit using a combination of four primitive geometric operations: translation, rotation, reflection, and glide reflection. According to group theory, different combinations of these four geometric operations lead to different symmetry groups. In this work, we select a single challenging ornament, and analyze it both from the theoretical point of view and perceptual point of view. We present the perceptual experiment results, where one can see that the symmetries that the participants perceived from the ornaments do not match to what the theory dictates.