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I believe that this is a doc error in V10 (this was programmed to be but not implemented). The new VoronoiMesh should work for 3D set of points.

The DelaunayMesh function works. Here is a doc example:

pts = RandomReal[{-1, 1}, {25, 3}];
DelaunayMesh[RandomReal[{-1, 1}, {25, 3}]]

enter image description here

But if you try:

pts = RandomReal[{-1, 1}, {25, 3}];
VoronoiMesh[pts]

You get the error: enter image description here

Docs for Voronoi say:

The cells will be intervals in 1D, convex polygons in 2D, and convex polyhedra in 3D.

Tested in V10.0.0 for Mac and Win.

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marked as duplicate by J. M. is away Feb 24 at 2:49

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    $\begingroup$ I have already talked about this here. I'm not so sure it is a bug, rather it has not been implemented but planned. Because internally the new Mesh functions rely on TetGen which supports 3D voronoi diagrams but somehow this functionality has been omitted. $\endgroup$ – RunnyKine Jul 15 '14 at 0:02
  • $\begingroup$ @Szabolcs no! Typo. $\endgroup$ – Murta Jul 15 '14 at 0:14
  • $\begingroup$ Not implemented in V10.0.1 yet $\endgroup$ – Murta Sep 17 '14 at 1:38
  • $\begingroup$ I didn't expect it to be implemented. When I asked about it in one of the online seminars they had, their response made me believe it will come in V11 or later. $\endgroup$ – RunnyKine Sep 17 '14 at 2:18

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