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Sebastien,
Thanks for your response!
There is no problem on CGAL side. 
I found the problem. The number of singular faces in this case was signficanly small than reported. 

On Friday, July 07, 2023 00:05 PDT, "Sebastien Loriot" ( via cgal-discuss Mailing List) <> wrote:
 
> ">It should indeed be partition as the classify() function for each facet
> gives a unique result.
>
> Maybe if you want a complete example I can compile and run, I can have a
> look and tell you if it is a bug in CGAL or in your code.
>
> Best,
>
> Sebastien.
>
> On 7/7/23 02:43,  wrote:
> > It is not clear to me of a facet belongs exclusively to one of the four
> > types.
> > I have
> > read https://doc.cgal.org/latest/Alpha_shapes_3/index.html#Alpha_shapes_3Definitions and section 2.3 of it. From that it appears it should be exclusive.
> > However the sum of number of diffrent types is not eqaul to the number
> > when no condtion is used. I modified the code below and executed it 5
> > times, four times for each type and then once without the "if" condition
> > so that all facets are counted.
> > ​​​​​​ Do I need to use infinite precesion for exact match?
> > Component 1 , general mode
> > Exterior 7208 ALL 67754
> > Interior 56668
> > 63876 diff 3878
> > Regular 3872
> > Singular 5450
> > 9322
> >
> >
> >
> >   double alpha = 0;
> >     Alpha_shape_3 as(points.begin(), points.end(), alpha, mode);
> >     Alpha_iterator opt = as.find_optimal_alpha(num_of_components);
> >     as.set_alpha(*opt);
> > *    Classification_type in_class_type = Classification_type::SINGULAR;*
> >     for (auto it = as.finite_facets_begin();
> >         it != as.finite_facets_end();
> >         it++)
> >     {
> >         auto class_type  = as.classify(*it);
> > *        if (in_class_type == class_type)*
> >         {
> >
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