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.
a sphere has 0 flat serfaces 0 vertices
cone
A a solid figure on a flat surface is a plane figure (I do believe)
A SPHERE has no vertices and no FLAT surfaces
the flat surfaces of a solid figure are the
a sphere has 0 flat serfaces 0 vertices
A sphere.
cone
A a solid figure on a flat surface is a plane figure (I do believe)
This is an impossibility. If it is a solid figure then it will have more than 1 surface. If it has only 1surface and it is a solid, then it must be a sphere, but the surface of a sphere is not flat is it? By using the word 'solid' then by definition, it is three dimensional and has thickness. A cylinder has no vertices , but it has 2flat surfaces. A vertex is a point where three lines meet, such as on a pyramid, which has 4 vertices. Have I forgotten something or is this a 'trick' question?
A SPHERE has no vertices and no FLAT surfaces
the flat surfaces of a solid figure are the
The flat surface of a solid figure is called a face. For example, a rectangular prism has 6 flat surfaces and therefore 6 faces.
Cone
circle
sphere
A face is the flat surface on a solid figure. For example, a triangular prism has five flat surfaces and therefore five faces.