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? ___ # 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