Three mirrors tilted to each other at a 60 degrees angle give an effect of infinite reflections.
Mirror system inside the kaleidoscope allows to multiply images of objects placed inside the device. It is also responsible for symmetry of received image.
Set the kaleidoscope in such a way so the whole field of view is evenly lit. Slowly rotate the kaleidoscope around its axis. Watch how the image transforms. Notice the symmetry of the image.