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[gwf421 <>]

>> P.make_triangle(p,q,r); 
>> std::cout << "H Edge info:" << std::endl; 
>> for ( Halfedge_iterator hit = P.vertices_begin(); hit !=
>> P.vertices_end(); ++v) 
>>        std::cout << hit->vertex()->point() << std::endl; 

The third line quoted above shows that you've passed a vertices_begin() to
Halfedge_iterator.
vertices_begin() returns an iterator of vertex, which is definitely
incompactable with a Halfedge_iterator receiver "hit".
Try the following:
for (Halfedge_iterator hit = P.halfedges_begin(); hit != P.halfedges_end();
++hit)

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