No, a cone has one vertex.
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it has one vertex two circle edges and one face
one face one vertex and two circle edges * * * * * What kind of cone is that? It has 1 edge, 2 faces (one curved and one plane), and 1 vertex.
A traditional cone has two faces but in fact it is a truncated cone. It has no verticles although it does have a vertex.
A cone only has 1 vertex because it only has one point where it connects. (vertex=a point)
A cylinder has two bases that are circles but a cone only has one base then a vertex.