Dome with hexagons

With the exception of dodecahedron, it is impossible to cover the entire surface of a sphere with pentagons only, but you can do it with a mixture of hexagons and pentagons, and with many other shapes. These domes are called geodesic grids. You can make these domes easily with the help of free Rhino plugins called Rhinopolyhedra (Polyhedron command) and Rhinowaterman (WatermanPolyhedron command).
Rhinopolyhedra plugin is here:
Rhinowaterman plugin is here:

Grids made of hexagons and pentagons are called Goldberg polyhedra. The best example is soccer (football) ball. Rhinopolyhedra plugin calls them “Dual Geodesic Icosahedron Patterns.” The following pictures are examples of the Goldberg polyhedra.