Generally, an edge is a straight line between two points or vertices, like on a square or cube. Since a cone doesn't have any of these, I would say 0 edges. Similarly, since a face is usually supposed to be flat, I would say 1 face (the curved part doesn't count).
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1 edge, 2 faces, no vertices
2 faces, 1 edge, 0 vertices
A cone hasEdges-1Vertices-1Faces-2
2 edges 2 faces 1 vertices
2 faces, 1 edge and 1 vertex.