Pendentives

A pendentive is a curved, triangular vault segment that transfers the weight of a dome to the supporting piers below. It forms the transition from a circular dome to a polygonal base—typically a square—allowing a dome to be set over a room with a square plan.

Geometrically, each pendentive is a concave surface that projects inward from the corner of a square bay toward the dome's apex, created by the intersection of a hemisphere with the supporting walls. Collectively, four pendentives brace the dome and distribute its load to the four piers, creating a large, open interior.

Pendentives originated in late antique Byzantine architecture; the 6th-century Hagia Sophia in Constantinople is the landmark early example, where a vast dome seems to rest on a square base. The technique was later adopted throughout the Byzantine world and was widely employed in Western Europe and in Islamic architecture to crown ambitious domes, mosques, and mausoleums.

Pendentives are often contrasted with squinches, another method to place a circular dome on a square base. Squinches bridge the gap with stepped or arched elements at the corners, whereas pendentives rise directly from the square corners and slope to meet the dome.