Polymnia, in Greek religion, one of the nine Muses, patron of dancing or geometry. She was said in some legends to have been the mother of Triptolemus, the first priest of Demeter and the inventor of agriculture, by Cheimarrhus, son of Ares, god of war, or by Celeus, king of Eleusis. In other versions, she was the mother of Orpheus, the legendary lyre-playing hero, or of Eros, the god of love.