A cylinder would fit the given description
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sphere
The geometrical object known as a cone has no planar faces, two curved surfaces, no edges and one vertex. A "real" object often called a cone is a portion of a half cone. That has one base, a curved surface, and one vertex.
A cone - although a face is generally taken to be a plane surface, not a curved one.
It has 6 faces and 12 edges
There is only 1 curved face!