This bronze sculpture by Giovanni Battista Foggini is dated c. 1690. It is located in the Metropolitan Museum of Art in New York. It depicts the hero standing, in military garb, in the act of committing suicide by plunging a sword into his chest.
The work is entitled "The Suicide of Ajax".
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"Ajax or Aias ... was a mythological Greek hero, the son of King Telamon and Periboea, and the half-brother of Teucer. He plays an important role in Homer's Iliad and in the Epic Cycle, a series of epic poems about the Trojan War...
Like most of the other Greek leaders, Ajax is alive and well as the Iliad comes to a close. Later, when Achilles dies, killed by Paris (with help from Apollo), Ajax and Odysseus are the heroes who fight against the Trojans to get the body and bury it next to his cousin, Patroclus. Ajax, with his great shield and spear, manages to drive off the Trojans, while Odysseus pulls the body to his chariot, and rides away with it to safety. After the burial, both claim the armor for themselves, as recognition for their efforts. After several days of competition, Odysseus and Ajax are tied for the ownership of the magical armor which was forged on Mount Olympus by the god Hephaestus. It is then that a competition is held to determine who deserves the armor. Ajax argues that because of his strength and the fighting he has done for the Greeks, including saving the ships from Hector, and driving him off with a massive rock, he deserves the armor. However, Odysseus proves to be more eloquent, and the council gives him the armor. Ajax, "Unconquered", and furious, falls upon his own sword, "conquered by his [own] sorrow".
In Sophocles' play Ajax, a famous retelling of Ajax's demise takes place—after the armor is awarded to Odysseus the hero Ajax is so insulted, that he wants to kill the sons of Atreus (Agamemnon and Menelaus). But Athena intervenes and clouds his mind and vision. He goes to a flock of sheep and slaughters them, imagining they are the Achaean leaders, including Odysseus and Agamemnon. When he comes to his senses, covered in blood, and realizes that what he has done has diminished his honor, and he decides that he prefers to kill himself rather than live in shame. He does so with the same sword Hector gave him when they exchanged presents. From his blood sprang a red flower, as at the death of Hyacinthus, which bore on its leaves the initial letters of his name Ai, also expressive of lament. His ashes were deposited in a golden urn on the Rhoetean promontory at the entrance of the Hellespont.
Ajax's half-brother Teucer stood trial before his father for not bringing Ajax's body or weapons back where Teucer was acquitted for responsibility but found guilty of negligence. He was disowned by his father and wasn't allowed back on Salamis Island.
The suicide of Ajax
Homer is somewhat vague about the precise manner of Ajax's death but does ascribe it to his loss in the dispute over Achilles' shield; when Odysseus visits Hades, he begs the soul of Ajax to speak to him, but Ajax, still resentful over the old quarrel, refuses and descends silently back into Erebus.
Like Achilles, he is represented (although not by Homer) as living after his death in the island of Leuke at the mouth of the Danube. Ajax, who in the post-Homeric legend is described as the grandson of Aeacus and the great-grandson of Zeus, was the tutelary hero of the island of Salamis, where he had a temple and an image, and where a festival called Aianteia was celebrated in his honour. At this festival a couch was set up, on which the panoply of the hero was placed, a practice which recalls the Roman Lectisternium. The identification of Ajax with the family of Aeacus was chiefly a matter which concerned the Athenians, after Salamis had come into their possession, on which occasion Solon is said to have inserted a line in the Iliad (2.557–558), for the purpose of supporting the Athenian claim to the island. Ajax then became an Attic hero; he was worshiped at Athens, where he had a statue in the market-place, and the tribe Aiantis was named after him. Pausanias also relates that a gigantic skeleton, its kneecap 5 inches (13 cm) in diameter, appeared on the beach near Sigeion, on the Trojan coast; these bones were identified as those of Ajax."