Technically, there's no shape with no surface and no vertices, but a sphere is close. It has no vertices but has just one surface.
An ovoid (egg-shape) is one possible answer. A smooth blob (to use a very technical term!) is another.
Cube
A cylinder would seem to fit the given description
a cylinder l
Zero vertices
0 vertices 0edges 2 flat surfaces
A cylinder has 2 surfaces (faces), 0 vertices, and 0 edges.
A sphere or torus (a donut).
Not in Euclidean geometry.
circle
A SPHERE has no vertices and no FLAT surfaces
triangular prism
A cube has 4 flat surfaces (called faces) and 6 vertices (or corners).
The cube have: -- six (6) faces -- twelve (12) edges -- zero (0) curved surfaces -- eight (8) vertices
6 flat surfaces - known as faces, 12 edges 8 vertices.
Vertices = 4Faces = 4 Edges = 6.
An ovoid (egg-shape) is one possible answer. A smooth blob (to use a very technical term!) is another.