After being outwitted by the clever Odysseus, then taunted by him from the ship as it sails away from the land of the Cyclopes, Polyphemus appeals to Poseidon, his father, to make certain that if Odysseus does, in fact, make it home, it is after an agonizingly long journey and one in which he loses all of his companions.
Polyphemos' request of Poseidon is central to Odysseus' travels. He first prays that Odysseus never reach home. He then asks that if Poseidon cannot fulfill this wish, that Odysseus come home "late and come a broken man - all his shipmates lost, alone in a stranger's ship - and let him find a world of pain at home! (lines 592-5)" This prophesy is repeated by Tiresius, and at the time Odysseus tells his tale to Alcinous, Odysseus has already lost all his ships and men, and it appears he will return to Ithaca in a Phaecian ship.
The manner in which Polyphemos frames his request is important. He identifies Odysseus by name, by his epithet ("raider of cities"), his patronymic ("Laertes' son") and his home. This is to ensure that Poseidon's curse falls precisely on the right man.
After Odysseus and his men trick and then blind the Cyclops Polyphemus, he prays to his father, Poseidon, the god of the sea and earthquakes, and asks him to put a curse on Odysseus and his men.
Poseidon is angered at Odysseus and does what his son requests, and Odysseus and his men are plagued by Poseidon for the rest of their journey.
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