I also found this strange, but I think the example is much harder to understand than the article claims.
By my current interpretation:
If the light shines in all directions, then a regular polygon, or in fact any convex polygon, doesn't need the mirrors to illuminate the room - the candle will light the room without needing a bounce. So, if you're thinking of a convex polygon, it's not quite relevant to this example.
The only difficult case would be if there was a concave polygon and the light had to bounce into the "caves" (or perhaps a series of rooms).
It's possible to imagine that there are specific set-ups where, if the mirrors are set up just right, the light will be bounced back out of a cave rather than filling it up.
If such a situation exists, then that bounce back would happen only with a very precise set-up: being arbitrarily close to the set-up wouldn't result in the bounce back.
By my current interpretation:
If the light shines in all directions, then a regular polygon, or in fact any convex polygon, doesn't need the mirrors to illuminate the room - the candle will light the room without needing a bounce. So, if you're thinking of a convex polygon, it's not quite relevant to this example.
The only difficult case would be if there was a concave polygon and the light had to bounce into the "caves" (or perhaps a series of rooms).
It's possible to imagine that there are specific set-ups where, if the mirrors are set up just right, the light will be bounced back out of a cave rather than filling it up.
If such a situation exists, then that bounce back would happen only with a very precise set-up: being arbitrarily close to the set-up wouldn't result in the bounce back.