One.
But it is a bit tricky and depends on how you define an edge.
Many use the definition of a boundary of a geometric figure
Please see the link to the math forum at Drexel University.
There is a lengthy discussion of this topic.
A cone has one flat face, one curved face, one vertex and one curved edge.
One.
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It has 0 sides
A cone has one vertex, one edge and two faces.
A solid cone has 2 faces and 1 edge
A cylinder and a cone - are two entirely different 3D shapes. A cylinder has three faces & two edges. A cone has two faces and one edge.