Pendentives transition Hagia Sophia’s square base into its circular dome. These curved, triangular sections of a spherical surface allow a round dome to rest above four supporting piers arranged as a square.
Each pendentive narrows toward the corner below and broadens upward toward the circular springing of the dome. This geometry redirects the dome’s weight into the four major piers and helps manage the outward forces produced by the immense roof structure.
The present Hagia Sophia was built under Emperor Justinian I after the Nika riots and was completed in 537. Its architects, Anthemius of Tralles and Isidore of Miletus, made exceptionally ambitious use of pendentive construction. The result created a vast central space whose dome appears to float above a ring of windows.
Squinches are the main alternative people commonly confuse with pendentives. A squinch uses an arch, corbel, or small vault across a corner to change a square plan into an approximately polygonal one. Pendentives are curved spherical triangles and provide the distinctive transition used beneath Hagia Sophia’s great dome.