A pyramid with a four sided base has five faces and five corners.
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A pentagonal prism * * * * * No. A pentagonal prism has 7 faces and 10 vertices! A rectangular pyramid has 5 faces and 5 vertices.
A tetrahedron; a shape made of four triangles.
A sphere has no faces an corners. The term "faces" and "corners" are applied to polyhedrons, figures with flat surfaces.
No corners, two faces
No such shape exists. The closest contenders would be: a cylinder - 3 faces, 2 edges, 0 verticies or a cone - 2 faces, 1 edge, 1 vertex