octagonon

Greek okto meant eight and gōnia meant angle. An octagonon was an eight-angled figure. The regular octagon is notable for a practical property: it is the regular polygon closest to a circle that can be made from a square by cutting the four corners at 45 degrees. This practical relationship — octagon from square — made it an accessible shape for builders who needed to approximate circular spaces.

Byzantine church architecture used the octagonal plan extensively. The Dome of the Rock in Jerusalem (691 CE), the Baptistery of Florence (begun 11th century), and the Castel del Monte in Apulia (1240s) are all octagonal or octagonally planned. The octagonal dome became the standard solution for topping a square structure — the pendentives and squinches that bridge a square plan into an octagon and then into a circle are Byzantine and Islamic architectural innovations.

Stop signs are octagons. The 1954 Vienna Convention on Road Signs established the octagonal stop sign as an international standard, chosen because it is recognizable in any orientation and distinguishable from other road signs. A driver approaching a stop sign from any direction can identify it by shape before reading the text.

The UFC (Ultimate Fighting Championship) fighting cage is called the Octagon — a trademarked name for the eight-sided chain-link fence that replaced the boxing ring. The shape was chosen in 1993 by UFC co-founder Art Davie because it eliminated the corners that a rectangular ring creates, giving fighters no structural advantage from cornering an opponent.