Cupola

As the original author of this question, I must apologise for getting it somewhat wrong.

A cupola (according to Wikipedia) is "a relatively small ... tall structure on top of a building. Often used to provide a lookout or to admit light and air, it usually crowns a larger roof or dome."

The ellipsis in the above definition marks where I've extracted the words "most often dome–like".

Wikipedia depicts several examples of cuploas (cupolae?), not all of which are dome–shaped.

Dictionary.com gives three definitions under the heading 'Architecture':

1 (a):	a light structure on a dome or roof, serving as a belfry, lantern, or belvedere
1 (b):	a dome, especially one covering a circular or polygonal area
2:	any of various domelike structures

So ... a cupola, while often shaped as a dome, is not necessarily a dome. Not only that, but asking someone to define a cupola as the answer to a quiz question is probably asking a bit too much.