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A compound shape comprising a cylinder and a cone. There is no single name for such a shape.
There is no specific name.There is no specific name.There is no specific name.There is no specific name.
According to the strictest definition of "face" being a flat surface, a cone has one. This leaves no name for the other part of the cone which is a curved surface. Some people call this a face as well.
The solid you are describing is called a cylinder. It has two circular faces, one curved face, and no vertices.
You could call the vertex, the apex, the tip, or the point of the cone.