A cube and a cuboid of which both have 8 vertices, 12 edges and 6 faces
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Cylinders have no vertices since the entire object is rounded. Only objects in which two lines meet in the same planar are are considered to have vertices.
The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.
2 faces can't share the same face, and they cannot share ALL vertices and edges either
Those would be called similar solids.
"Vertices" means "vertexes". "Vertex" means one of the triangle's points. The triangle has three points. When you talk about two or three of them, you're talking about 2 or 3 'vertices'.