Being an animator, I found this highly amusing. This was listed as the oldest machine there: the praxinoscope. The faceted nature of the mirrors gives off the same effect as a shutter for film -- this is important as it is needed in order to give off the optical illusion of 'persistence of vision'. The images projected from the drum onto the mirrors will look like the girl's jumping rope, instead of becoming a big blur.
It was so cool to watch one of these for reals.