Cf. asymmetrical. What’s the difference?

Maybe see http://wikidiff.com/unsymmetrical/asymmetrical

Examples:

- As for symmetry: again, spiders are quite symmetrical, while some flowers, such as orchids, are very unsymmetrical, yet we do not find them any less attractive for that. So I do not think that symmetry, colour and contrast are all that we are seeing in flowers when we imagine that we are seeing beauty. (Deutsch - Infinity)

- Powered by liquid-fueled motors, the fuels and oxidizers in question were dangerous, corrosive chemicals—unsymmetrical dimethyl hydrazine and nitrogen tetroxide—and the fact that they were called “storable” liquids was a relative statement. (Clancy - All Fears)