This was not really clear, but fiterator means face iterator, and a face is a triangle. Org, Dest and Apex are the indices of those vertices.
for(Delaunay::fIterator fit = delobject.fbegin();
fit != delobject.fend();
++fit)
{
cout << " Org " << delobject.Org(fit) << ", "
<< " Dest " << delobject.Dest(fit) << ", "
<< " Apex " << delobject.Apex(fit) << //" \t: Area = "
}
Don't forget Triangle++ doesn't really require you to put the actual Triangle.c code, so it was really easy to use.