About three or four years ago, I implemented the Delaunay and Voronoi tessellations in [Haskell](https://github.com/stla/qhull), with the help of the **Qhull** C library. Now I reimplement it in R.

I have noticed that including or not the degenerate tiles of the Delaunay tessellation has a serious influence on the Voronoï tessellation obtained by duality.

For example, this is the Voronoï diagram (restricted to its bounded cells) of a dodecahedron surrounded by three pairwise perpendicular dashed circles, when I include the degenerate Delaunay tiles:

[![enter image description here][1]][1]

And here is the result when I don't include the degenerate tiles: 

[![enter image description here][2]][2]

How can one explain this difference?

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# EDIT

Here is a picture of the object from which I take the Delaunay tessellation, except this is a dodecahedron instead of a tetrahedron:

[![enter image description here][3]][3]


  [1]: https://i.sstatic.net/gknKj.gif
  [2]: https://i.sstatic.net/dZfOI.gif
  [3]: https://i.sstatic.net/lIBYI.png