A plane.
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A contradiction. A solid is a 3-dimensional object, a face is 2-dimensional. Hence you cannot have a solid face.
The flat surface of a solid figure is called a face. For example, a rectangular prism has 6 flat surfaces and therefore 6 faces.
The solid you are describing is called a cylinder. It has two circular faces, one curved face, and no vertices.
A face is a flat surface. The only solid with no flat surfaces is a sphere.
A cube is one of them