Turkish triangle

The Turkish triangle is a transition system used to set a dome over a square room. Instead of the single smooth spherical surface of a pendentive, it uses a band of faceted triangles, flat planes folded against each other, set side by side in the corners. It runs like a belt at the top of the walls, just below the base of the dome, and is common in Anatolian Seljuk and early Ottoman buildings.

Role in the building

It does the same job as a pendentive or a squinch: turning a square base into the circular or polygonal ring the dome sits on, and bringing the dome’s weight down through the corners into the walls. The difference lies in the geometry. Building with flat triangular faces is easier in stone and brick than laying a true spherical surface. The triangles narrow downward in the corners and, at the top, complete the circle of the dome base. From outside, this belt can read as a faceted drum below the dome.

• Corner triangles: the main pieces filling each corner
• Intermediate triangles: completing the ring at mid-wall
• Dome springing: the circular base resting on the band

Survey and 3D modeling

Because it is made of flat facets, the Turkish triangle looks easier to measure and draw than a pendentive. In historic buildings, though, the faces are rarely perfectly flat and the triangles are seldom identical. Extract each corner separately from the point cloud. In a 3D model, a single polyhedral band is enough to show the real folds hidden under the plaster, and restitution work should also look into the band’s original plaster and decoration.