Symmetry and beauty are often claimed to be linked, particularly by mathematicians and scientists. However philosophers and art historians seem generally agreed that although symmetry is indeed attractive, there is also a somewhat sterile rigidity about it, which can make it less attractive than the more dynamic, less predictable beauty associated with asymmetry. Although a little asymmetry can be beautiful, an excess merely results in chaos. As Adorno suggested, asymmetry probably results most effectively in beauty when the underlying symmetry upon which it is built is still apparent. This paper examines the ways in which asymmetries, particularly left-right asymmetries, were used by painters in the Italian Renaissance. Polyptychs often show occasional asymmetries, which are more likely to involve the substitution of a left cheek for a right cheek, than vice-versa. A hypothesis is developed that the left and right cheeks have symbolic meanings, with the right cheek meaning ‘like self’ and the left cheek meaning ‘unlike self’. This principle is evaluated in pictures such as the Crucifixion, the Annunciation and, the Madonna and Child. The latter is particularly useful because the theological status of the Madonna changed during the Renaissance, and her left–right portrayal also changed at the same time in a comprehensible way. Some brief experimental tests of the hypothesis are also described. Finally the paper ends by considering why it is that the left rather than the right cheek is associated with ‘unlike self’, and puts that result in the context of the universal ‘dual symbolic classification’ of right and left, which was first described by the anthropologist Robert Hertz.