Rules · Domes · Façades · Plans
Crown the four corner bays of a cross-in-square with smaller domes on drums around the great central dome, making a five-domed quincunx.
The five-domed arrangement goes back to Justinian’s church of the Holy Apostles in Constantinople, where five domes stood over the arms and crossing of a Greek cross; San Marco in Venice was modelled on it. In the middle Byzantine cross-in-square the smaller domes moved to the corner bays, giving the familiar pyramid of one tall and four lower domes.
Five domes were read as Christ and the four Evangelists. In Russia the quincunx became the standard crown of cathedrals, from the Dormition in the Moscow Kremlin onward.
To set a round dome on a square bay, imagine a sphere passing through the four corners of the square; cut it by the four vertical planes of the sides and by the horizontal plane of their crowns. The four spherical triangles left in the corners are the pendentives; the circle at their top carries the dome.
sphere radius R = S⁄√2; arches = sphere ∩ side planes (radius S⁄2); ring at h₀ + S⁄2 with radius S⁄2
Throw an arch diagonally across each upper corner of the square, backed by a small conch or cone; the four squinches and the four walls between them make an octagon, on which a round dome can sit.
octagon side = S (√2 − 1) ≈ 0.414 S; squinch span = octagon side
If the sphere that forms the pendentives is simply continued above the ring, the bay is covered by a single shallow dome, the sail vault or pendentive dome, which springs directly from the four corners.
crown = h₀ + S⁄√2 (lower than a hemisphere on the ring, h₀ + S)
Lift the dome on a cylindrical or polygonal drum pierced with windows between the ring of the pendentives and the springing of the dome, to light the centre of the church and to make the dome visible from afar.
drum height ≈ ⅓–1 × its radius (Byzantine); much taller in Russian churches
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.
Hagia Sophia: 40 windows and 40 ribs; dome ≈ 31 m across, crown 55.6 m above the floor
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.
Hagia Sophia: central square 31 m; two semidomes of radius ≈ 15.5 m; four exedrae; interior ≈ 31 × 70 m
Cite this page Chris Paton, “Five domes in a quincunx”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/quincunx-five-domes. Text, drawings and models licensed under CC BY-NC 4.0.