The shape that is commonly known as a cone has two faces, one vertex and one edge.
Mathematically, however, the cone has infinite height and so has one [curved] face and one vertex.
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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.