Polemarchus or Polemarch (died 404 BC) was the son of Cephalus

Cephalus

Cephalus is an Ancient Greek name, used both for the hero-figure in Greek mythology and carried as a theophoric name by historical persons. The word kephalos is Greek for "head", perhaps used here because Cephalus was the founding "head" of a great family that includes Odysseus...

 of Syracuse. He had two brothers, Lysias

Lysias

Lysias was a logographer in Ancient Greece. He was one of the ten Attic orators included in the "Alexandrian Canon" compiled by Aristophanes of Byzantium and Aristarchus of Samothrace in the third century BC.-Life:According to Dionysius of Halicarnassus and the author of the life ascribed to...

 and Euthydemus

Euthydemus

-People:*Euthydemus , a fleet commander for Athens during the Sicilian Expedition, 415 to 413 BC*Euthydemus, son of Cephalus, mentioned in Plato's Republic...

, and a sister who married Brachyllus. Polemarchus and Lysias traveled to Thurii

Thurii

Thurii , called also by some Latin writers Thurium , for a time also Copia and Copiae, was a city of Magna Graecia, situated on the Tarentine gulf, within a short distance of the site of Sybaris, whose place it may be considered as having taken...

 when the latter was 15 years old.

Polemarchus was an Athenian philosopher and was singled out by the Thirty Tyrants

Thirty Tyrants

The Thirty Tyrants were a pro-Spartan oligarchy installed in Athens after its defeat in the Peloponnesian War in 404 BC. Contemporary Athenians referred to them simply as "the oligarchy" or "the Thirty" ; the expression "Thirty Tyrants" is due to later historians...

 for being a wealthy metic

Metic

In ancient Greece, the term metic referred to a resident alien, one who did not have citizen rights in his or her Greek city-state of residence....

. Unlike his brother, he did not manage to escape and was executed by being forced to drink hemlock. Melobius, one of the Thirty Tyrants, snatched the golden earrings from Polemarchus' wife. After Polemarchus' death, the Thirty forbade his family from holding a funeral in any of their houses. Plato

Plato

Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

's Republic is set at Polemarchus' house in the Piraeus

Piraeus

Piraeus is a city in the region of Attica, Greece. Piraeus is located within the Athens Urban Area, 12 km southwest from its city center , and lies along the east coast of the Saronic Gulf....

, which was located next to their shield manufacturing store that employed 120 skilled slaves. Polemarchus himself speaks briefly in Book 1 of the Republic.