2 edges (curved), 0 corners, and 3 faces (one of which is not flat)
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A cylinder has 0 vertices (corners), 0 edges, and 2 faces.
If you need convincing, my proof is Euler's formula, which which relates all three and is true for all solids in Euclidean 3-space:
V + F - E = 2
0 + 2 - 0 = 2
You cannot consider the curved boundaries when counting faces or edges.
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A sphere has no edges, because an edge is defined as where two faces meet. Likewise, it has no faces, because a face is defined as the flat surface of an object. Likewise, it has no corners either.
no edges and 4 corners
A sphere has no faces an corners. The term "faces" and "corners" are applied to polyhedrons, figures with flat surfaces.
No corners, two faces
A parallelogram is a 2-dimensional object and so has only one face.