(Πολυξένη), a daughter of Priam and Hecabe (Apollod. 3.12.5). She was beloved by Achilles, and when the Greeks, on their voyage home, were still lingering on the coast of Thrace, the shade of Achilles appeared to them demanding that Polyxena should be sacrificed to him. Neoptolemus accordingly sacrificed her on the tomb of his father. (Eur. Hec. 40; Ov. Mct. 13.448, &c.) According to some Achilles appeared to the leaders of the Greeks in a dream (Tzetz. ad Lyc. 323), or a voice was heard from the tomb of Achilles demanding a share in the booty, whereupon Calchas proposed to sacrifice Polyxena. (Serv. ad Aen. 3.322.) For there was a tradition that Achilles had promised Priam to bring about a peace with the Greeks, if the king would give him his daughter Polyxena in marriage. When Achilles, for the purpose of negotiating the marriage, had gone to the temple of the Thymbraean Apollo, he was treacherously killed by Paris. (Hyg. Fab. 110.) Quite a different account is given by Philostratus (Her. 19. 11; comp. Vit. Apollon. 4.16), according to whom Achilles and Polvxena fell in love with each other at the time when Hector's body was delivered up to Priam. After the murder of Achilles Polyxena fled to the Greeks, and killed herself on the tomb of her beloved with a sword. The sacrifice of Polyxena was represented in the acropolis of Athens. (Paus. 1.22.6. comp. 10.25.2.)
[L.S]A Dictionary of Greek and Roman biography and mythology
Smith, William
A Dictionary of Greek and Roman biography and mythology. William Smith, LLD, ed. 1890