Hagia Sophia, Constantinople
Anthemius and Isidore’s church (532–537, dome rebuilt 558–562): a dome on pendentives ringed by 40 windows, extended east and west by semidomes and exedrae.
The rules it illustrates
A ring of windows at the foot of the dome. Pierce the base of the dome with a close ring of windows between buttressing ribs, so that the shell seems to float on light rather than to rest on the arches.
Semidomes lengthen the dome. To turn a domed square into a long church, open two of its great arches into semidomes of the same radius, and open the semidomes in turn into smaller exedrae, so that the space expands by stages from the central dome.
Buttress the dome where the semidomes cannot. Where no semidome takes the thrust of the dome, on the north and south, carry it across the aisles to massive buttress piers that rise above the roofs, and fill the great arches with thin walls pierced by windows.
Make a shallow dome steeper. A shallow dome pushes harder outward than a steep one of the same span: when the first dome of Hagia Sophia fell, it was rebuilt with a higher rise so that its thrust would be more nearly vertical.
Where it appears in the book
In the styles Byzantine.
In the chapters Domes, Byzantium and the Early Church.