I was going through the documentation of Mathematica but couldn't find any built-in function that can find all possible triangulations for a given set of points.

For example, if I have the following points which are the vertices of unit square,


Then, I want Mathematica to print that there are two triangulations and also give the explicit triangulations.

The above example was straightforward as it involved 2-D points. I'm looking for something in Mathematica which can do the above task for higher-dimensional points as well.

I know this can be done in the software TOPCOM using the commands points2triangs and points2ntriangs, but I wanted to know whether such a thing is implemented in Mathematica as it is done in SageMath

  • $\begingroup$ Look at DelaunayMesh $\endgroup$ Oct 3 '21 at 13:39
  • $\begingroup$ @DanielHuber That will produce one triangulation. OP wants all triangulations. $\endgroup$
    – Szabolcs
    Oct 3 '21 at 14:52
  • $\begingroup$ @Szabolcs, yes, I want all possible triangulations. Any idea whether it is possible on Mathematica yet? $\endgroup$
    – Epsilon
    Oct 3 '21 at 15:06
  • $\begingroup$ @Epsilon I am not aware of such functionality in Mathematica, but it is quite possible that I missed something that was recently added. You could write an interface to TOPCOM ... $\endgroup$
    – Szabolcs
    Oct 3 '21 at 15:39

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