1. the quality of being made up of exactly similar parts facing each other or around an axis. “this series has a line of symmetry through its center”
Similar: regularity, evenness, uniformity, equilibrium, consistency, congruity, conformity, agreement, correspondence, orderliness, equality.
2. correct or pleasing proportion of the parts of a thing. “an overall symmetry making the poem pleasant to the ear”
Similar: balance, proportions, regularity, evenness of form, harmony, harmoniousness, consonance, concord, coordination
Symmetry is an interesting concept to ponder as a photographer. Is the aesthetic of a perfectly symmetrical photograph interesting to you? I have to admit that I have no absolutely symmetrical photos in my collection. There is symmetry to be found in nature, but it’s rarely exact. It has been said that when judging “attractiveness” in people, facial symmetry features highly. But no one’s face is exactly symmetrical.
I would venture that exact symmetry is static and not very interesting. To me, it’s the juxtaposition of similar things or balanced things that are in fact different that is most interesting.
I think that Nature in balance is the highest example of beauty, and its type of symmetry is not architectural and mathematic except on a very cellular level. When you look at the big picture, that precision is subdued. When humans step in, they tend to force that uniformity in a way that often destroys Nature’s beauty. (If I had a photographic example of agricultural monocultures and row housing, I’d insert it here.)