A new methodology for understanding the construction of Extended Goldberg polyhedra has been developed on the basis of Goldberg polyhedra by using our methods of the ‘spherical rotating’ and the ‘spherical stretching’. The spherical rotating describes the deformation of rotating polygons on a sphere; the spherical stretching depicts the deformation of stretching spaces between polygons on a sphere. Our results show that these Extended Goldberg polyhedra are a kind of novel geometrical objects of icosahedral symmetry and are considered to explain some viral capsids.