From Penguin Dictionary of Architecture

A vault of even curvature erected on a circular base. The section can be segmental, semicircular, pointed, or bulbous.

If a dome is to be erected on a square base, members must be interpolated at the corners to mediate between the square and the circle. They can be pendentives or squinches. A pendentive is a spherical triangle; its curvature is that of a dome whose diameter is the diagonal of the initial square. The triangle is carried to the height which allows the erection on itstop horizontal of the dome proper. A squinch is either an arch or arches of increasing radius projecting one in front of the other, or horizontal arches projecting in the same manner. If squinches are placed in the corners of the square and enough arches are erected on them they will result in a suitable base-line for the dome. In all these cases the dome will have the diameter of the length of one side of the square. It can be placed direct on the circular base-line, when this is achieved, or a drum, usually with windows, can be interpolated. If the dome has no drum and is segmental, it is called a saucer dome. If it has no drum and is semi-circular, it is called a calotte.

Another method of developing a dome out of a square is to take the diagonal out of the square as the diameter of the dome. In this case the dome starts as if by pendentives, but their curvature is then continued without any break. Such domes are called sail vaults, because they resemble a sail with the four corners fixed and the wind blowiing into it.

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Note added at 11 hrs (2008-06-23 21:43:51 GMT)
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costoloni - ribs
A projecting band on a ceiling or vault, usually structural but sometimes purely decorative