Polyphêmos is the Kyklops son of the god of the sea and earthquakes, Poseidon. Polyphêmos lives with other Kyklopês, giant one-eyed creatures, in the Land of the Kyklopês. Odysseus negatively describes Kyklopês as "giants, louts, without a law to bless them" (148). Polypêmos lives in solidarity in his cave, mending to his sheep. Not a follower of the Guest Law, Polyphêmos dismisses Odysseus when he explains it is a Grecian "custom to honor strangers" (153). Polyphêmos then explains he does not fear Zeus and does not intend to aid Odysseus or his men. The cannibalistic cave-dweller devours Odysseus's men on multiple occasions as below:
When Polyphêmos traps Odysseus and his remaining men in the cave, Odysseus gets Polyphêmos drunk and he and his men gauge his eye out as depicted below in an amphora from around 520 BCE:
It is also depicted in this Laconian kylix (cup) from 520 BCE:
Odysseus has told Polyphêmos his name is Nohbdy, so when Polyphêmos says "Nohbdy's ruined me," his neighbors think everything is fine (157). Odysseus eventually outwits the Kyklops and escapes. Then Odysseus reveals his true name while sailing away. Polyphêmos promises he will actually help Odysseus, but Odysseus refuses, and Polyphêmos, and in turn Poseidon, become enraged at Odysseus.
-CB