A prytaneion was the seat of the prytaneis, and so the seat of government in ancient Greece. The term is used to describe any of a range of ancient structures where officials met, but the term is also
Prytaneion of Panticapaeum, II b.c. (Kerch, Crimea)
In ancient Greek religion and mythology, Hestia is the virgin goddess of the hearth and the home. In myth, she is the firstborn child of the Titans Cronus and Rhea, and one of the Twelve Olympians.
Prytaneion
…this fire was kept was the prytaneion, and the chieftain (the king or prytanis) probably made it his residence. The building contained the holy fire of Hestia, the goddess of the hearth, and symbol of the life of the city. The term prytanis (pl. prytaneis) is generally applied specially to those who, after…
Hestia holding a branch of a chaste-tree, red-figure kylix, attributed to Oltos, Tarquinia National Museum
Hestia (?) on the northern frieze of the Siphnian Treasury, 6th century BC, Delphi Archaeological Museum, Greece
Fragment of a Hellenistic relief (1st century BC – 1st century AD) depicting the twelve Olympians carrying their attributes in procession; Hestia with scepter to the left, from the Walters Art Museum