CUPOLA. - It is a domical vault with a semicircular profile—raised, depressed, or pointed—resulting from the rotation of polycentric curves, intended to cover a space of square, circular, or polygonal plan.

In Asia Minor, on the other hand, the dome was first inserted into the Anatolian-type basilica covered by a barrel vault and then into cruciform schemes; in the course of its evolution, Byzantine architecture increasingly developed the drum pierced by windows and made the system of thrust equilibrium more and more complex. The series of Constantinopolitan churches (SS. Sergio e Bacco, S. Sofia, S. Irene, S. Teodosia, S. Giovanni in Trullo, S. Maria Diaconissa, S. Maria Panachrantos, S. Maria Pammacharistos, S. Salvatore in Chora) demonstrates the high degree of perfection achieved by Byzantine builders.
In Italy, during the Romanesque period, true domes depended on Byzantine and Moorish examples or influences, and in such cases show the extrados of the vault on the exterior (S. Marco in Venice, the cathedral of Pisa, S. Ciriaco and S. Maria in Porto Nuovo in Ancona, the cathedral of Caserta Vecchia, the cathedral of Molfetta, S. Giovanni degli Eremiti, and S. Cataldo in Palermo, the Annunziata in Messina, etc.). In longitudinal buildings of the Lombard type, being segmented and set on an octagonal base and not visible on the exterior, they take on rather the character of tiburi (v.). In the 14th century, the prevalence of Gothic taste developed the tiburio almost to the limit of the irrational, which, in order to define the interior space according to a precise geometric shape, achieves effects of a completely particular nature; of great interest therefore appears the plan of S. Maria del Fiore prepared for a dome-like covering over the central space grafted onto the triple nave. And at the beginning of the 15th century rises the agile dome, with a pointed arch section and double shell held together by ribs that limit the eight segments; the work still bears the mark of Gothic taste in various elements, but in the definition of the enclosed and precise space
it announces the new times. The dome designed by Alberti for the Tempio malatestiano, as appears from the medal by Matteo de Pasti, was hemispherical on the model of the Pantheon. Domes multiplied during the 15th century; the Madonna dell'Umiltà in Pistoia, S. Maria delle Carceri in Prato, S. Maria delle Grazie al Calcinaio, S. Maria del Popolo and S. Maria della Pace in Rome are all inspired by a lively sense of line that accentuates their vertical thrust and elegance.
With Bramante, both in the tempietto of S. Pietro in Montorio and in the project for S. Pietro, the shell rests on the drum, losing all vertical thrust, with a sense of heaviness that in the second case the drum pierced with an open loggia would have accentuated. The history of the dome is summarized in that of S. Pietro, in which the Sangallesco project, while developing the drum to the point of partially concealing the shell, gives it a greater development than a semicircle. Thus is prepared the triumphant Michelangelo solution of a double-shell dome which allows, in addition to exceptional stability, a greater external thrust and a more coherent definition of the internal space, since the first shell is set somewhat lower. The plastic power of the drum serves to effectively buttress the thrusts of the dual shell, while the expansive breadth of the interior space dominates that of any other room, subordinating it to itself in a synthesis that allows no deviations. Alongside the greatest 16th-century example, one can recall those of the sanctuary of Loreto, S. Biagio in Montepulciano, S. Maria di Loreto in Rome, S. Maria di Carignano in Genoa, or the Redentore in Venice, which is more faithful to the Bramantesque spirit than to Michelangelo's innovation. But already in Vignola’s Il Gesù in Rome, the diameter of the dome becomes greater than the width of the nave so as to enhance with its

Among the nineteenth-century c. inheriting the tradition, one may mention those of the Gran Madre di Dio in Turin, of S. Carlo in Milan, of S. Francesco di Paola in Naples, etc. Then the new technique, pushed to its extreme consequences, leaves in S. Gaudenzio in Novara a curious example of a multi-tiered drum that falls short of the purposes and effects required of a true and proper c. With the change in spatial sensibility, c. seem destined to decline with the prevalence of reinforced concrete; then new interpretations of Romanesque tiburia re-emerged from the formal multiplicity of nineteenth-century and modern eclecticism, and finally some further c. in the wake of sixteenth-century tradition. - See plates LXIX-LXXII.