Domes do not have to be perfectly spherical in cross-section, however; a section through a dome may be an ellipse. If the baseline is taken parallel to the shorter of an ellipse's two diameters, a tall dome results, giving a sense of upward reach. A section across the longer axis results in a low dome, capping the volume instead. A very low dome is classified as a saucer dome. All the surfaces of any dome are curved. A spectacular innovation, one that is at the heart of Baroque style, is the oval dome, which gives axial direction and movement to the space beneath it. Though the oval dome is typically identified with churches of Bernini and Borromini, the first oval dome was erected by Vignola for a chapel, Sant'Andrea in Via Flaminia often called Sant'Andrea del Vignola. Julius III commissioned the dome in 1552 and construction finished the following year. The largest oval dome was built in the basilica of Vicoforte by Francesco Gallo.
Domes that have been disproportionately influential in later architecture are those of the Pantheon in Rome, Hagia Sophia in Istanbul (or in that time Constantinople), and the Dome of the Rock in Jerusalem. In Western architecture, the most influential domes built since the Renaissance have been those of St. Peter's Basilica in Rome and Jules Hardouin-Mansart's dome at Les Invalides in Paris. The dome of St. Paul's Cathedral in London was the inspiration for the United States Capitol in Washington, which in turn inspired domes of most of the US state capitols.
A cathedral is often referred to as a duomo in Italian or "dom" in German. This is not because so many are crowned with crossing domes over the space where transepts intersect the nave, but instead stemming from the Latin noun "domus", house, or in this case the "domus dei", the house of God. A dome is a mark of palatial ambitions whenever it is seen crowning a residence. The first residential domes were seen in Nero's Domus Aurea that covered the slope of the Palatine Hill, built after the Great Fire of Rome of AD 64 with a lavishness that scandalized the senatorial class.
In the 20th century, thin "eggshell" domes of pre-stressed concrete by architect-engineers such as Nervi opened new directions in fluid vaulted spaces enclosed beneath freeform domed space which now might be supported merely at points rather than in the traditional constricting ring.
A dome can sit directly on a circular base, however, this is not possible if the base is square. The concave triangular or trapezoidal sections of vaulting that provide the transition between a dome and the square base on which it is set and transfer the weight of the dome are called pendentives. (A less sophisticated version of a pendentive is a squinch.) Under the dome illustrated at left, the pendentives bear circular medallions in bas relief. A pendentive is a constructive device permitting the placing of a circular dome over a square room or an elliptical dome over a rectangular room. The pendentives, which are triangular segments of a sphere, taper to points at the bottom and spread at the top to establish the continuous circular or elliptical base needed for the dome. In masonry the pendentives thus receive the weight of the dome, concentrating it at the four corners where it can be received by the piers beneath. Prior to the pendentive's development, the device of corbelling or the use of the squinch in the corners of a room had been employed. The first attempts at pendentives were made by the Romans, but full achievement of the form was reached only by the Byzantines in Hagia Sophia at Constantinople (6th cent.). In the simple dome the pendentives are part of the same sphere as the dome itself, however such domes are rare. In the more common compound dome the pendentives are part of the surface of a sphere of larger radius than the dome itself but whose center is at a point lower than that of the dome. Another alternative is for a drum to be inserted between the dome and pendentives. Pendentives were commonly used in Byzantine, Renaissance and baroque churches.
Many domes are topped by a lantern, a structure with openings (or windows) to admit light in the cupola.
Many sports stadiums are domed, especially in climates that have widely-variable summer and winter weather. The first such stadium was the Astrodome in Houston, Texas. A major improvement to the domed stadium was accomplished with the construction of SkyDome, now Rogers Centre, in Toronto, Ontario, the first domed stadium with a retractable roof.
A saucer dome is the architectural term used for a low pitched shallow dome which is described geometrically as having a circular base and a segmental (less than a semicircle) section. A section across the longer axis results in a low dome, capping the volume. A very low dome is a saucer dome. Many of the largest existing domes are of this shape.
Gaining in popularity from the 18th century onwards, the saucer dome is often a feature of interior design. When viewed from below it resembles the shallow concave shape of a saucer. The dome itself, being often contained in the space between ceiling and attic, is invisible externally. These domes are usually decorated internally by ornate plaster-work, occasionally they are frescoed.