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A ruled surface is called a generalized cylinder if it can be parameterized by, where is a fixed point. A generalized cylinder is a regular surface wherever. The above surface is a generalized cylinder over a cardioid. A generalized cylinder is a flat surface, and is sometimes called a "cylindrical surface" or "cylinder surface"

A generalized cylinder need not be closed

Kern and Bland define a cylinder as a solid bounded by a generalized cylinder and two parallel planes. However, when used without qualification, the term "cylinder" generally refers to the particular case of a right circular cylinder.