The sixth century christ icon from the monastery of st. catherine at mt. sinai is a good example of perfect symmetrical balance

Not really, if you look at the icon, it's for centered towards the left side, Jesus' right hand is infront of his chest with his index and middle finger curled, and he is holding a book, most likely the Holy Testaments, to his chest. His robe on his right shoulder is slightly disheveled, and his left eye is larger. His ears are at different heights, indicating his head is at an angle.