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About three or four years ago, I implemented the Delaunay and Voronoi tessellations in Haskell, 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

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

enter image description here

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

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