The Pendentive: the Trick That Put a Dome on Four Piers

A pendentive is a curved, triangular vault surface in the corner between two arches. Four pendentives together turn the square opening between four arches into a round ring, and on that ring a dome can rest. The pendentive solved one of architecture's hardest problems: how to put a round dome over a square room, carried by four piers instead of a round wall. The great example is Hagia Sophia in Istanbul from 537, and ever since the pendentive has carried the domes of Byzantine churches, Renaissance churches and Baroque cathedrals.

Facts

The Problem: a Round Dome on a Square

A dome is an arch that has been rotated about its central axis, and it wants to stand on a round foot. The simplest way is therefore to build a round wall and lay the dome on top. That is what the Romans did in the Pantheon in Rome, completed around 125: the dome is about 43 metres in diameter and rests on a cylindrical wall thick enough to take its thrust. The room is round, and there are no corners to resolve.

But a round wall closes the space. Anyone who wanted a dome in the middle of a larger church, with arms or aisles opening in several directions, had to place it on four arches resting on four piers. The opening under the dome is then square, and in the corners four empty triangles arise between the arches. The question is what is to fill them.

One answer was the squinch: a small vault or niche laid obliquely across the corner, so that the square becomes an octagon and the octagon almost a circle. The squinch was used in Persia and in Byzantium and later in Islamic and Romanesque architecture. In the monastery church of Hosios Loukas in Greece, from the early 11th century, the dome rests on eight arches in this way. The pendentive was the other answer, and the more elegant one.

How a Pendentive Works

Imagine a hemisphere placed over a square, so large that the corners of the square lie on the rim of the sphere. Cut away everything that sticks out beyond the four sides of the square. What remains is four arches along the sides and between them four curved triangles that narrow downwards towards the corners. Then cut off the top at the level of the crowns of the arches. What remains is a round ring carried by the four triangles, and those are the pendentives. On the ring a new dome can be built.

The pendentives lead the weight of the dome down into the four piers, but the dome also pushes outwards round its whole foot, just like an arch. Something is therefore needed to take up the thrust: heavy walls, half domes, buttresses or iron rings. The drawing of the dome in Florence below shows how Brunelleschi held his dome together with chains of stone, wood and iron.

In a Byzantine church interior the pendentive also has a place in the pictorial programme. Christ as the ruler of all, Pantocrator, sits in the dome, the Mother of God in the apse and the four evangelists on the pendentives, as the four cornerstones between heaven and earth.

Hagia Sophia: the Dome That Seems to Hang in Light

Emperor Justinian had Hagia Sophia built in Constantinople in five years, 532–537. He engaged not ordinary master builders but two learned men, the mathematician Anthemius of Tralles and Isidore of Miletus. The dome rests on four great arches and four pendentives, and to east and west the space is extended by two half domes that take up the thrust and make the church an elongated domed basilica.

At the foot of the dome is a ring of windows between forty ribs. The light that streams in makes the dome seem to float, and contemporaries wrote that it seemed to hang on a chain from heaven. The first dome collapsed in 558 after earthquakes and was replaced by a higher and steeper one. To the top it is today about 55 metres, which you can compare with the Pantheon and other buildings in the height chart below. For almost a thousand years Hagia Sophia was the world's largest church.

After Hagia Sophia the dome on pendentives became the core of the Byzantine church. The domes became smaller but more numerous, and they were often raised on a drum with windows. St Mark's in Venice, begun in 1063, is a Greek cross with five domes on pendentives, modelled on the Church of the Holy Apostles in Constantinople.

The Renaissance and the Baroque: the Dome on a Drum

The architects of the Renaissance took up the pendentive again. Brunelleschi used it on a small scale in the sacristy of San Lorenzo in Florence, with round medallions in the corner fields. His great dome over Florence Cathedral, on the other hand, rests on an octagonal drum above the crossing, and no pendentives were needed there.

In St Peter's in Rome the arrangement became classical: four enormous piers, four arches, four pendentives with medallions of the evangelists, a tall drum with windows and at the top Michelangelo's dome with lantern. The dome reaches 136 metres. The same structure, with the pendentives as the link between the square and the circle, is found in a long series of Baroque churches.

St Paul's Cathedral in London, built 1675–1710 to Christopher Wren's designs, has a dome over the crossing that is really three: an inner dome, a cone of brick that carries the lantern and an outer dome of timber and lead. In Sweden the dome came with the Baroque. Katarina Church in Stockholm, designed by Jean de la Vallée and begun in the 1650s, has a large dome over the crossing.

How to Recognise a Pendentive

Stand under the dome and follow the arches. If the room under the dome is square and you see four curved triangles in the corners that narrow downwards, they are pendentives. If the corners are instead bridged by small vaults or niches, so that you see an octagon, they are squinches. If the dome stands on a round wall as in the Pantheon, there is no transition at all.

Look also at what is on the pendentives. Evangelists, prophets or angels in medallions are a sure sign that the architect wanted to show the transition, not hide it. The pendentive and the dome are explained in the basics on arches and vaults, and the Byzantine churches in the guide to Byzantine architecture. How vaults work in general is described in the guide to vaults and arches, and the terms are in the glossary.

Look Out For

Exercise

What problem does a pendentive solve?