The class Triangulation_utils_3 defines operations on the indices of vertices and neighbors within a cell.
#include <CGAL/Triangulation_utils_3.h>

 
In dimension 3, index of the neighbor n that is next to the current cell,
when turning positively around an oriented edge whose endpoints are
indexed i and j. According to the usual numbering of
vertices and neighbors in a given cell, it is also the index of the vertex
opposite to this neighbor n. (see Figure ). Precondition: ( i < 4 ) && ( j < 4 ) && ( i != j ).  

 
Has a meaning only in dimension 2. Computes the index of the vertex that is next to the vertex numbered i in counterclockwise direction. (see Figure ). Precondition: i<3.  

 
Same for clockwise. 
Figure: Operations on indices.