A cone is the answer but it’s not obvious because of dubious definitions of vertexes, edges and faces.

The reason to argue that a cone is the answer is that its two faces are the flat circle at its base and the curved surface. Its one edge is where the curved surface meets the base and its one vertex is the point of the cone.

The reason this is a contentious question (just type it in to Google to see debate raging about it) is that it’s hard to get a definitive explanation of the terms.

An edge is a line where two faces come together; that is true of the cone. A vertex is the corner point of a polygon; also true of a cone.

An edge is a one-dimensional line segment joining two adjacent zero-dimensional vertices in a polygon. Is this true of a cone’s curved surface?

So that is the debate. But if you think about it, how can anything else be the answer?

If you have a pint then you must have at least two faces. These cannot be joined to form an edge without creating another.

Test it on a piece of paper, draw a vertex first. It should look something like this: ^.

Now extend your lines so you have two clear faces.

Great, now how are you going to create an edge? Link the two surfaces of course.

But now you have a triangle and that means you are looking at three faces.

Only a cone will allow you to create a vertex and an edge by linking them with only one face.

The reason to argue that a cone is the answer is that its two faces are the flat circle at its base and the curved surface. Its one edge is where the curved surface meets the base and its one vertex is the point of the cone.

The reason this is a contentious question (just type it in to Google to see debate raging about it) is that it’s hard to get a definitive explanation of the terms.

An edge is a line where two faces come together; that is true of the cone. A vertex is the corner point of a polygon; also true of a cone.

An edge is a one-dimensional line segment joining two adjacent zero-dimensional vertices in a polygon. Is this true of a cone’s curved surface?

So that is the debate. But if you think about it, how can anything else be the answer?

If you have a pint then you must have at least two faces. These cannot be joined to form an edge without creating another.

Test it on a piece of paper, draw a vertex first. It should look something like this: ^.

Now extend your lines so you have two clear faces.

Great, now how are you going to create an edge? Link the two surfaces of course.

But now you have a triangle and that means you are looking at three faces.

Only a cone will allow you to create a vertex and an edge by linking them with only one face.