The concept TriangulationDSVertexBase_2 describes the requirements for the vertex base class of a Triangulation_data_structure_2<Vb,Fb>.
Note that if the Triangulation_data_structure_2 is plugged into a triangulation class, the vertex base class has additional geometric requirements depending on the triangulation class.
At the base level, provides access to one of its incident face through a Face_handle.
Since the Triangulation_data_structure_2 is the class which defines the handle types, the vertex base class has to be somehow parameterized by the triangulation data structure. But since the Triangulation_data_structure_2 itself is parameterized by the face and vertex base classes, there is a cycle in the definition of these classes. In order to break the cycle, the base classes for faces and vertices which are plugged in to instantiate a Triangulation_data_structure_2 use a void as triangulation data structure parameter. Then, the Triangulation_data_structure_2 uses a rebind mechanism (similar to the one specified in std::allocator) in order to plug itself as parameter in the face and vertex base classes. This mechanism requires that the base class provides a templated nested class Rebind_TDS that itself provides the subtype Rebind_TDS<TDS2>::Other which is the rebound version of the base class. This rebound base class is the class that the Triangulation_data_structure_2 actually uses as a base class for the class of Triangulation_data_structure_2::Vertex.
template <typename TDS2>  
TriangulationDSVertexBase_2:: struct Rebind_TDS  
This nested template class has to define a type Other which is the
rebound vertex base , where the actual
Triangulation_data_structure_2 is plugged in.
This type Other will be the actual base
of the class Triangulation_data_structure_2::Vertex.

typedef TriangulationDataStructure_2  
Triangulation_data_structure;  
typedef TriangulationDataStructure_2::Vertex_handle  
Vertex_handle;  
typedef TriangulationDataStructure_2::Face_handle  
Face_handle; 
TriangulationDSVertexBase_2 v;  
default constructor.
 
TriangulationDSVertexBase_2 v ( Face_handle f);  
Constructs a vertex pointing to face f.

void *  v.for_compact_container () const  
void * &  v.for_compact_container () 
CGAL::Triangulation_ds_vertex_base_2<Tds>
CGAL::Triangulation_vertex_base_2<Traits,Vb>
CGAL::Regular_triangulation_vertex_base_2<Traits,Vb>
CGAL::Triangulation_hierarchy_vertex_base_2<Vb>
CGAL::Triangulation_vertex_base_with_info_2<Info,Traits,vb>