The pendentive

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A spherical triangle that carries a circular dome on a square bay. Four arches are thrown across the sides of the square; the curved triangles left between them rise from the corners and close into a horizontal circle at the top, on which the dome sits. The device is what lets a dome be placed over a rectangular hall rather than over a circular drum, and it is therefore the enabling invention behind the whole Byzantine and later Ottoman tradition of centrally domed halls. Pendentives concentrate the dome's entire load and outward thrust onto four points, which is structurally elegant and unforgiving: the four piers and their buttressing become the building. The alternative solution, the squinch - an arch or niche bridging the corner - appears in Sasanian and later Islamic building and produces a visibly different geometry.