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A torus has one surface, no edges, no vertices.
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.
A sphere, an ellipsoid, a torus (donut), an irregular blob with no pointy bit.
A cylinder, a frustum, a sphere with two slices cut off, a torus (doughnut) with a wedge removed are some examples.
It has one face.