a cone has one flat surface one vertex and no edge.
An hemisphere is half of a globe with a circular flat base, a round edge, a curved surface but no vertices.
sphere, spheroid, ellipsoid
A pentagon is a polygon that has 5 sides, 5 vertices and a flat face
A prism with an n-sided base will have 2n vertices, n + 2 faces, and 3n edges. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges.
6 flat surfaces - known as faces, 12 edges 8 vertices.
If they are flat, they are faces. If they are pointed, they are vertices and if they are thin and long they are edges.
0 vertices 0edges 2 flat surfaces
Sphere
A torus has one surface, no edges, no vertices.
A sphere
Cool question. I think there are at least three: hemisphere, section of an obloid, cone. Since you did not say face, you appreciate difference between definitions in platonic solids as defined by Euclid and Euler, and the curved solids. A hemisphere has one flat surface and no vertices, but so does a cone. A vertex is defined as the meeting of edges, which are defined as straight in euclidean geometry. Since there are no straight edges coming to a point in a cone (unless you want to talk about infinite edges emanating from the flat surface), there are no vertices on a cone.