Rules · Plans · Domes · Vaults
Divide a square naos into nine bays: dome the central one on a drum over four columns, barrel-vault the four arms of the cross, and cover the four corner bays lower; add three apses to the east and a narthex to the west.
arms = central bay width; corners lower; dome on pendentives over four columns
The cross-in-square became the standard church of the Orthodox world after Iconoclasm. It is compact and hierarchical: the dome with its image of Christ over the centre, the arms of the cross rising to it, the lower corners stepping down, so that the outside reads as a pyramid of volumes and the inside as a cross inscribed in a square.
Its scale is intimate (many are under 15 m square) and its structure economical: four slender columns carry the dome on pendentives and arches, the barrel vaults of the arms buttressing the dome in four directions and being buttressed in turn by the corner bays.
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, “The cross-in-square: nine bays”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/cross-in-square. Text, drawings and models licensed under CC BY-NC 4.0.