I was trying to approximate the surface area of the sphere.  

I remember that Archimede approximated the circumference of a circle by calcualting the perimeter of its inscribed and circumscribed regular polygons while n ( number of sides of the polygon) increased.  

Anyway when I looked for a similiar procedure for the sphere, I discovered that there are only 5 convex regualar polyhedrons (platonic solids), so it doesn't seem to be possible to approximate the surface of the sphere with the same procedure.  

I then looked to Goldberg and Geodesic polyhedrons but I didn't understand really how they are constructed so I'm not convinced "they fit for the procedure."  

So I'm asking, if there are only 5 regular polyhedrons can be the sphere considered the limit of a regular polyhedron with infinite faces?  

If not, are Goldberg and Geodesic Polyhedrons the alternative to approximate the surface of a sphere?