Beautycheck is an interesting link. Whilst the face presented as an example is by no means ugly, neither is it that of a stunning beauty, IMHO. Of course the old saying "beauty is in the eye of the beholder", has a deep resonance of truth. Symmetry is a contributing factor to to the perseption of beauty, but I have also seen faces that are asymmetrical, or even badly scarred on one side, that I would still consider as stunningly beautiful.

Whilst symmetry does play a part, I think Beautycheck places a totally unrealistic emphasis on that aspect. Beauty is a  much deeper and incredibly more complex phenomenon than just symmetry alone.