Are the flat surface of a cylinder called faces?

Answer 1

The platonic solid definitions of face, edge and vertex only apply to polyhedra, where all edges are straight, all face are polygons, and all vertices are the meetings of straight edges. As a result, the term 'face' has to be redefined for solids with any curved surfaces. Different Math texts have different answers and some Geometry texts ignore the issue altogether.

One way to approach this is to call them surfaces when dealing with curved solids. Other mathematicians just define their terms at the beginning of the discussion and move on from there.