Is it possible to subdivide a revolved surface with a Goldberg polyhedra (hexagons+pentagons) in a way that the pentagon is located on the revolution axis?
A Goldberg polyhedron has icosahedral symmetry, so it cannot be a general revolved surface. For a sphere I believe Rhino Polyhedra will generate various Goldberg polyhedra.
If you are asking about more general shapes with hexagonal/pentagonal faces though -
If the target surface is close enough to a sphere, you could generate the subdivided mesh on a sphere then wrap it onto the target.
For more general shapes though, you will need not just pentagons but also some heptagons.
Here’s a way you can remesh to pentagons/hexagons/heptagons while keeping rotational symmetry:
revolve_symmetry.gh (13.8 KB)
Which version of Rhino are you running?
Those are native components, so the message should go away if you update.