a square
a rectange
a triangle
a hexagon
an octogon
a polygon
If you mean 1 flat surface and 1 vertex, then the only thing I can think of is a cone.
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Cone
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.
The only thing I can think of is a cone.
It has a flat base, a curved surface area, a circular edge and one vertex.
A cardioid is one possibility. See link, below.
A shape with 1 vertex, 1 edge, 1 flat face, and 1 curved face is a cone. The vertex is the tip of the cone, the edge is the circular base where the flat face meets the curved surface, and the flat face is the circular base itself. The curved face extends from the base to the vertex.
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.
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 face is the flat surface of an object (2 or 3 dimensional). An edge is when two sides (faces) meet on an object. A vertex is the corner of an object, where an angle exists between two or more lines.