In Greek mythology, Polyphemus (Ancient Greek Πολύφημος) son of Elatus is a Lapith hero from Larissa and an Argonaut — not the Cyclops of the Odyssey. He fought the Centaurs in his youth, sailed with Jason, and was left in Mysia searching for Hylas with Heracles; he founded Cius, ruled there, and later died in the land of the Chalybes still seeking his comrades.
Adapted from Wikipedia, "Polyphemus (Argonaut)" · CC BY-SA 4.0
I.Family
Polyphemus is son of the Lapith chief Elatus by Hippea and thus possibly brother of Caeneus, Ischys, and Ampycus. One source marries him to Laonome, sister of Heracles; in some accounts he is called the beloved of that hero.
Apollonius and Apollodorus place him among the Argonauts from Thessalian Larissa.
II.Mythology
As a Lapith he fought the Centaurs in his youth. In the Iliad Nestor numbers "the godlike Polyphemus" among an earlier generation of heroes who destroyed a savage mountain-dwelling tribe — an allusion Homer's audience would have recognized.
Years later he joins the Argonauts. In Bithynia he hears Hylas cry as the nymphs drag the youth away; helping Heracles search, both are left behind when the Argo sails on. Settling in Mysia he founds Cius and becomes its king. Later he sets out again to find his fellow Argonauts and dies in the land of the Chalybes, buried by the seashore under a poplar.
III.Homonyms
This atlas entry (polyphemus-elatid) is the Lapith Argonaut, son of Elatus and founder of Cius. He is strictly distinct from Polyphemus the Cyclops (polyphemus-cyclops), son of Poseidon and Thoosa, whom Odysseus blinds in the Odyssey.