The number of shapes that a ceiling can contain is limited only by the imagination of the builder. The shape of a ceiling as a whole is determined by the shape of the room that it is in, but within the ceiling other shapes can be formed by ridges and by decorative features.
Most flat ceilings don't have any decorative attributes, and are designed to fade into the background so that more attention is given to the walls, art and furnishings in a room. Because most rooms are square or rectangular, most flat ceilings are these shapes as well. Exceptions exist, such as the Oval Office in the White House, which of course has an oval ceiling. A drawback of flat ceilings with no features is that any damage or blemishes to the ceiling are much more visible.
Cathedral ceilings are installed directly beneath the rafters of a roof rather than underneath a series of flat joists. The result is a high, pointed ceiling that creates a roomy and airy space beneath it. Many cathedral ceilings feature exposed beams, a design accent that creates rows of elongated rectangles along the length of the ceiling. Interesting temporary shapes are created on cathedral ceilings by the movement of the sun as its light comes through the windows. Most cathedral ceilings are constructed of two facing rectangular planes. More rarely, all four sides of a room's ceiling will be brought to a point at the top, resulting in four converging triangles.
In some older mansions, fancy ceilings are decorated with hardwood or painted paneling. Some of these panels are built in a grid pattern of squares or rectangles, while the more elaborate ones may incorporate curved moldings, hexagons and other elaborate shapes. Paneled ceilings are very expensive to build, and are rarely seen in contemporary houses. The grids of rectangles in a dropped ceiling are geometrically similar to a paneled ceiling, although the effect that is created is very different. Dropped ceilings evoke office and institutional space, while paneled ceilings are the stuff of mansions and castles.
Domes create the most interesting shapes of any ceiling, because the ceiling and the walls are the same thing. In a classical dome such as the Pantheon in Rome, the dome is composed of a complex series of squares of decreasing size. In more modern incarnations of the dome such as Buckminster Fuller's geodesic dome, the overall shape is created by a series of triangles that are formed into alternating pentagons and hexagons. A full dome comprises one half of the interior of a sphere, and is a defining feature of classical architecture.