Polyxenus or Polyxeinus (Ancient Greek: Πολύξενος / Πολύξεινος) was son of Agasthenes (himself son of Augeas) and an Epeian leader at Troy. Homer numbers him among the four captains of the forty Epeian ships from Elis; Pausanias says he returned safely and named his son Amphimachus after the comrade who fell there. He is also counted among the suitors of Helen.
Adapted from Wikipedia, "Polyxenus" · CC BY-SA 4.0
I.Epeian command
In the Catalogue of Ships the Epeians muster forty vessels under four leaders beside Buprasium and the coast of Olympia. Godlike Polyxenus, son of king Agasthenes son of Augeas, commands one of those companies. Apollodorus and Hyginus count him among Helen's suitors, which explains his presence in the Trojan expedition.
Handbooks sometimes attribute the whole forty ships to him alone; Homer's wording distributes the Epeian fleet among Amphimachus, Thalpius, Diores, and Polyxenus.
II.Return
Pausanias, reading Homer against Elean memory, says Polyxenus came home alive from Troy and begat a son Amphimachus — a name given, he thinks, in honour of the Amphimachus son of Cteatus who did not return. Mother-names in later lists include Peloris.
III.Homonyms
This atlas entry (polyxenus-epeian) is Agasthenes' Trojan-war captain. A distinct earlier Polyxenus of Elis holds the Taphian cattle that Amphitryon ransoms; another Polyxenus (also called Medus) is son of Jason and Medea; a further Polyxenus ranks among the first priests of Demeter at Eleusis.