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Hi, every one,
 
Recently, I am studying mesh simplification and have learned the examples -- 
"edge_collapse_enriched_polyhedron" and "edge_collapse_polyhedron" -- in CGAL 
package. But when I try to add the simplification algorithm to the famous 
project appended with "A Tutorial on CGAL Polyhedron for Subdivision 
Algorithms", I found some problems.
 
If I declare a mesh use the Enriched_polyhedron template, then the sentence 
"SMS::Count_stop_predicate<EnrichedPolyIdMesh> stop2(1000);" will can not 
pass the compilation. Details list as follows:
 
typedef list:
typedef CGAL::Simple_cartesian<double> Kernel;
// define Surface as the example within CGAL
typedef CGAL::Polyhedron_3<Kernel> Surface;
// use Polyhedron_items_with_id_3 only
typedef CGAL::Polyhedron_3<Kernel, CGAL::Polyhedron_items_with_id_3> IdMesh; 
// use Enriched_items defined in the project
typedef CGAL::Polyhedron_3<Kernel, Enriched_items> EnrichedItemMesh;
// use mesh defined in the project
typedef Enriched_polyhedron<Kernel, Enriched_items> Mesh;                     
                   
// use Enriched_polyhedron and Polyhedron_items_with_id_3
typedef Enriched_polyhedron<Kernel, CGAL::Polyhedron_items_with_id_3> 
EnrichedPolyIdMesh; 

experiments and results:
    namespace SMS = CGAL::Surface_mesh_simplification ;
    SMS::Count_stop_predicate<Surface> stop(1000);                // pass
    SMS::Count_stop_predicate<EnrichedItemMesh> stop5(1000);      // pass
    SMS::Count_stop_predicate<IdMesh> stop3(1000);                // pass
    SMS::Count_stop_predicate<EnrichedPolyIdMesh> stop2(1000);    // error
    SMS::Count_stop_predicate<Mesh> stop4(1000);                  // error

From these experiments, we can found that the only difference between 
EnrichedItemMesh and Mesh lies in the difference between CGAL::Polyhedron_3 
and Enriched_polyhedron. However, Enriched_polyhedron is derived from 
CGAL::Polyhedron_3, why using Enriched_polyhedron will lead to error while 
using CGAL::Polyhedron_3 is correct?
 
Can anybody tell me some more information or advices on this problem?
Thank you in advance.
 
BTW, My programming environment is: Windows + VS2008 + CGAL3.3.1.

Lucida