CGAL users discussion list

[Olivier Devillers <>]

Le 5/27/11 2:50 PM, Yohann a écrit :
> I've looked for an answer to this question on the forum and google but I
> haven't found anything that seemed relevant (or I did not understand why it
> was relevant).
>
> I am willing to build a 3D triangulation with constrained faces (and not
> segments). I've read that the constrained 3d triangulation problem has no
> solution, but I'm not sure this result applies to the case where you
> constrain faces and not just segments.
>
> Can anyone point me to a page where a demonstration prooves that you can't
> constrain faces?

Schönhardt polyhedron cannot be triangulated
[E. Schönhardt. Über die Zerlegung von Dreieckspolyedern in Tetraeder. 
Math. Ann., 98:309–312, 1928.]

If you constrained only edges then you can triangulate [some paper of 
Shewchuk]