If you mean 1 flat surface and 1 vertex, then the only thing I can think of is a cone.
Cone
A cardioid is one possibility. See link, below.
The object described is a cone. A cone has one vertex (the point where the flat face meets the curved surface) and one flat face (the circular base). Due to its shape, a cone can roll along a flat surface smoothly.
It has a flat base, a curved surface area, a circular edge and one vertex.
If you mean 1 flat surface and 1 vertex, then the only thing I can think of is a cone.
Cone
A cardioid is one possibility. See link, below.
5
a square a rectange a triangle a hexagon an octogon a polygon
The object described is a cone. A cone has one vertex (the point where the flat face meets the curved surface) and one flat face (the circular base). Due to its shape, a cone can roll along a flat surface smoothly.
a cone has one flat surface one vertex and no edge.
It has a flat base, a curved surface area, a circular edge and one vertex.
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?
There can be no such shape. If there were a shape with n flat surfaces, then if you sliced off one vertex, you would have a shape with n+1 flat surfaces. So it is always possible to add one more flat surface.
a oval or heart
Cone