If you consider the textbook definition, an edge is the line where two faces meet and faces are always flat surfaces. A vertex is the point where three edges meet. Given these definitions, cylinders and cones have neither vertices or edges.
But I know that the point of a cone is called a vertex, because the axis of a cone is a line through the vertex and the center of the base. If the point of a cone is a vertex, then do cones and cylinders have edges?
I looked on the web (Math Forum) and found that the textbook definitions are for polyhedra, i.e. 3D shapes made up of only flat faces. The problem is that there is no other word to label the place where the flat face meets the curved face on either a cylinder or a cone. Math Forum recommended extending some definitions: edges would still be the line where two faces meet but we could have a "curved edge" (both words are necessary). A face is flat but we could have a "curved face" (again, both words necessary). So a cylinder would have two faces and one curved face, and two curved edges but no vertex. A cone would have one face and one curved face, one curved edge, and a vertex. But this seems a bit confusing for me, let alone the kids.
So does anyone else have any definitive mathematical terms or solutions to this?
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