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A cone is a three-dimensional geometric figure that has one flat face (the base), which is typically circular, and one curved surface that tapers to a point, which is the apex or vertex of the cone.
Therefore, in the context of faces as flat surfaces, a cone has only 1 face. If you consider the curved surface to be a "face," then it could be described as having 2 surfaces, but conventionally, only the flat, base circle is considered a face.