CGAL 5.5.2  2D Triangulations on the Sphere

#include <CGAL/Triangulation_on_sphere_face_base_2.h>
Fb.
The class Triangulation_on_sphere_face_base_2
is a model for the concept TriangulationOnSphereFaceBase_2
. It is the default face base class for triangulations on the sphere.
Triangulation_on_sphere_face_base_2
can be simply plugged into the triangulation data structure of a triangulation, or used as a base class to derive other base face classes tuned for specific applications.
Traits  must be a geometric traits class. The geometric traits is actually not used by the class. 
Fb  has to be a model of the concept TriangulationDSFaceBase_2 and will serve as a base class for Triangulation_on_sphere_face_base_2 . By default this parameter is instantiated by Triangulation_ds_face_base_2<> . 
CGAL::Triangulation_ds_face_base_2<Tds>
CGAL::Triangulation_face_base_with_info_2<Traits,Tds>
CGAL::Triangulation_on_sphere_vertex_base_2<Traits,Vb>
CGAL::Triangulation_on_sphere_2<Traits,Tds>