A circle or a sphere :)
What solid has 1 face 0 edges and 0 vertices?
Sphere
A sphere
There are many such figures, most of them nameless. A sphere, ellipsoid, and torus are among them. Any solid enclosed only by a curved surface can have your description.
All solid objects have to have edges,sides,length,width,depth,thickness. Even if the human eye can not detect it or your senses not feel it. Just my opnion. : )