In architecture, a triangular segment of a spherical surface that forms the transition between the circular plan of a dome and the polygonal plan of its supporting structure. The problem of placing a round dome on a square base assumed growing importance to Roman builders, but it remained for Byzantine architects to recognize the possibilities of the pendentive and fully develop it (seeHagia Sophia). One of the great architectural inventions of all time, the pendentive became very important in the Renaissance and Baroque periods. As a result of Byzantine influence, pendentives are also frequent in Islamic architecture. The vaulting form in which the curve of the pendentive and dome is continuous is known as a pendentive dome.