Yes, the point on the cone is a vertex.
Typical math textbooks define a cone as "A solid figure with one circular face and one vertex." So yes, there is one vertex.
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A cone has one vertex.
on the top
A cone has 1 vertex, 1 circular edge and 2 faces
A+: cone
sphere has 1 face and no vertex and it rolls but cone has 2 faces and it can roll and it has 1 vertex