Dr. Stickler in the hall of mirrors
Lets continue right where we left of on the previous page: Dr. Stickler between two mirrors. It is notieceable that there are two distinct versions of Dr. Stickler: one corresponds to the original, whereas the other looks like his mirror image. The following applet highlights the distinction using different colors. Due to the many reflections, even the number of reflection axes does increase. Next to the two original mirrors, there are "reflected mirrors", "reflected reflected mirrors" and so on. In the drawing, all symmetry axes have been included in the image (which one has to imagine extended to infinity on both sides). If we add two additional mirrors above and below Dr. Stickler, the resulting pattern will again repeat over the whole plane. Again there are two kinds of Dr. Stickler. The red ones have the same orientation as the original, while the green ones are mirror images. It is as if Dr. Stickler were standing in a room with four reflecting walls: in every direction he can see copies of himself. This last example is (after the "Attack of the Stickler-Clones" on the previous page) the second example of a so called wallpaper group or crystallographic group. We'll get to know more such groups later on. Das letzte Beispiel stellt (nach unserem "Angriff der Stickler-Klone" aus der letzten Seite) das zweite Beispiel einer so genannten Ornamentgruppe oder kristallographischen Gruppe dar. Wir werden später noch mehrere solcher Gruppen kennen lernen.Download files:
Two translations
Contents 
Angled mirrors 