Pendentives and Squinches
The Romans, the first true masters of arched construction, developed the groin vault to overcome the limitations of the tunnel vault (see Roman Architecture).
If one strips away the ceiling from a groin vault, one is left with four arches that form a square.
Instead of a groin vault, this supportive framework can alternatively be covered with a dome. This presents the interesting technical challenge of connecting something round to something square, whether the dome is set directly on the supportive frame or raised upon a cylindrical drum.
The initial solution was to build ordinary walls above the arches, creating a square surface. A dome could then be placed on this surface, though it would lack support at the corners of the square. This was rectified by adding a small arch to the inside of each corner; each arch is known as a squinch.1
Though squinches solve the problem of connecting a dome to a square frame, a much more elegant solution was developed by the Byzantines. Instead of building ordinary walls above the four-arch frame, they filled the spaces between the arches with walls in the shape of spherical triangles. Each of these walls is called a pendentive.1