SymmyS is any form of poetry whose organizing principle is rigid phonetic symmetry. The symmetry rule can apply to specific kinds of sounds (vowels, rhythm, consonants) or to every sound in a word. In all cases phonetic symmetry is an approximation, since true sound symmetry rarely exists in language.
SymmyS was invented by Thomas Mills Hinkle and named by Aren Emigh. The poetic form is a refinement of symmetrical techniques occasionally found in golden age poets. More specifically, the idea of the symmetrical line was first inspired by an observation in a remarkable book of criticism by Dámaso Alonso on Luis de Góngora's great baroque work, El Polifemo.
See http://tommyrot.arrr.net for the symmys home page and a detailed explanation of SymmyS rules and examples.