Dome
Dome, in architecture, hemispherical structure evolved from the arch, usually forming a ceiling or roof. Domes first appeared as solid mounds and in techniques adaptable only to the smallest buildings, such as round huts and tombs in the ancient Middle East, India, and the Mediterranean. The Romans introduced the large-scale masonry hemisphere. The dome exerts thrusts all around its perimeter, and the earliest monumental examples, such as the Roman Pantheon, required heavy supporting walls.
Byzantine architects invented a technique for raising domes on piers, permitting lighting and communication from four directions. The transition from a cubic base to the hemispherical dome was achieved by four pendentives, inverted triangular masses of masonry curved both horizontally and vertically, as shown in the figure. Their apexes rested on the four piers, to which they conducted the forces of the dome; their sides joined to form arches over openings in the four faces of the cube; and their bases met in a complete circle to form the dome foundation. The pendentive dome could rest directly on this circular foundation or upon a cylindrical wall, called a drum, inserted between the two to increase height.
Hagia Sophia
Displaced architecturally by the light, vertical styles of Gothic architecture, the dome regained popularity during the European Renaissance and Baroque periods. Vaulting is simpler than doming, and so the effort and ingenuity devoted to doming rectangular structures must be explained principally by the symbolic character of the dome. The desire to observe tradition preserved the dome in the early era of iron and steel construction. The modern reinforced concrete slab used in vaulting can be curved in length as well as width to form a dome. Here the distinction between vaults and domes has lost its original significance, being based only on the type of curvature in the slab.
The geodesic dome is built up of triangular or polygonal facets that distribute stresses within the structure itself.