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cylinders only have two faces.
two of the faces of a cylinder are circles circles have an infinite number of lines of symmetry therefore cylinders have an infinite number of planes of symmetry
You can find a polyhedron with any number greater than 4 of vertices or faces. However, a torus, ellipsoid, sphere, paraboloid, hyperboloid are all standard shapes with no vertices. Cylinders, too, have no vertices. And there are many completely random shapes - a lump of putty, for example, which will have no vertex.
10 faces 10 faces
A cube has 12 edges and cylinders have 2 edges.