Kaleidoscopes
What happens if one were to use not only two but three mirrors? There are only few possible ways to align these mirrors in such a way that they form a triangle where every corner angle is a fitting angle (i.e. a divisor of 180°): The angle sum in a triangle is 180°, so the only possible combinations are (60°, 60°, 60°), (90°, 45°, 45°) and (90°, 60°, 30°). The following three applets demonstrate the resulting three wallpaper groups.(60°, 60°, 60°)
(90°, 45°, 45°)
(90°, 60°, 30°)
Dr. Stickler can be moved around in each of these applets. In real life it lokks like this:
Download files:
Angled mirrors
Contents 
Wallpaper groups 