Pendentive is a curved, triangular architectural element that transitions a square or polygonal base into a circular dome, allowing the dome’s weight to be transferred efficiently to supporting piers or walls. It is a key feature in domed structures from Byzantine architecture onward, most famously used in Hagia Sophia in Istanbul (completed 537 AD), where four pendentives support the massive central dome.

Ribbed cupolas evolved from this principle, particularly in medieval Europe. The Aquitainian cupola at the Abbey Church of St. Front in Périgueux (11th century) exemplifies the early use of pendentives and ribbed construction. The intersecting arches in later Gothic architecture—such as those in the cathedrals of Angers and Laval—developed directly from the pendentive system, transforming the dome’s structural logic into a lightweight, ribbed vault. These ribs act as a skeletal framework, distributing thrust to four points of support, marking a direct lineage from the pendentive cupola to Gothic vaulting.

In later architecture, such as St. Peter’s Basilica in Rome (1540s), massive pendentives support a large dome, with their surfaces adorned by mosaics to channel structural forces. The pendentive rib cupola thus represents a foundational innovation in architectural engineering—bridging Byzantine dome design with the development of Gothic and Renaissance vaulting systems.