Thus the basic elements of the representation are vertices and faces. Each triangular face gives access to its three incident vertices and to its three adjacent faces. Each vertex gives access to one of its incident faces and through that face to the circular list of its incident faces. The edges are not explicitely represented, they are only represented through the adjacencies relations of two faces.
The triangulation classes of CGAL depends on two template parameters. The first template parameter stands for a geometric traits class which is assumed to provide the geometric objects (points, segments and triangles) forming the triangulation and the geometric predicates on those objects. The second template parameter stands for a model of triangulation data structure acting as a container for faces and vertices while taking care of the combinatorial aspects of the triangulation.
CGAL::Triangulation_euclidean_traits_2<R>
CGAL::Triangulation_euclidean_traits_xy_3<R>
CGAL::Regular_triangulation_euclidean_traits_2<Rep,Weight>
CGAL::Triangulation_2<Traits,Tds>::Face
CGAL::Triangulation_2<Traits,Tds>::Vertex
CGAL::Weighted_point<Pt,Wt>
CGAL::Triangulation_cw_ccw_2