A sloop is a great circle on a sphere. A shalfloop is an oriented sloop. It is always paired with a shalfloop whose supporting Sphere_circle is pointing in the opposite direction. The twin() member function returns this shalfloop of opposite orientation. Each Nef_polyhedron_S2 can only have one sloop (resp. two shalfloops).
The figure below depicts the relationship between a shalfloop and sfaces on a sphere map.
#include <CGAL/Nef_polyhedron_S2.h>
The following types are the same as in Nef_polyhedron_S2<Traits>.
There is no need for a user to create a SHalfloop explicitly. The class Nef_polyhedron_S2<Traits> manages the needed shalfloops internally.

 the mark of se . 

 the sphere circle of se . 

 the twin of se . 

 the incident sface of se . 
CGAL::Nef_polyhedron_S2<Traits>::SFace
CGAL::Nef_polyhedron_S2<Traits>::Sphere_circle