cone
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No. If it is a finite cone it has an edge - circular or elliptical, depending upon the plane that terminates it. If it is not a finite cone, it does not have a flat edge.
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A cone has 1 face, 0 edges, and one vertex. The face is the circular flat area. The cone can roll, so it has no edges. Edges have to be straight. The vertex is the pointy thing opposite to the face.
0 vertex edges and 1 base.
0 edges 0 faces (faces are planar bounded by linear edges) 2 curved surfaces 1 vertex
An infinite cone.
cylinder