I tried to solve that question out of interest, and thought I might create a Voronoi mesh, cut it into a circle, and color the mesh cells. But if I ask `VoronoiMesh`

Create cells for too many points `MeshCellCount[mesh, 2]`

(or equivalent `Length @ MeshCells[mesh]`

) returns a number less than the number of points initially specified.

I tried to use different functions to generate the points around which the cells should be built, using both exact and real numbers and checking out the documentation `VoronoiMesh`

and `MeshRegion`

but I'm still not sure what causes that. Are my points just too close together? `VoronoiMesh`

uniquely determine a cell for some of them?

The simplest code that reproduces this is:

```
MeshCellCount[
VoronoiMesh[
Flatten[Quiet[Thread[CirclePoints[Range[100], 360]]], 1]],
2]
```

This should return 36,000, as there are 100 radial points and 360 azimuthal points, instead 35,985. For this code it seems to start when there are about 32,000 elements. When the radial point points inwards `offer`

set to 87, I get the expected result. If the radial points are set to 88 (with the same 360 azimuthal points), I get an unexpected result. For all smaller numbers, it seems to work as expected.

If I use the following code to determine the number of cells, for some reason, this discrepancy will be displayed even with a smaller number of cells.

```
to generate[i_] : =
table[
{r Sin[[Theta]], r Cos[[Theta]]},
{[Theta]0, 359 [Pi]/ 180, [Pi]/ 180}
{r, 1/2, (i - 1) + 1/2}
]66 * 360 - MeshCellCount[VoronoiMesh[Flatten[generate[66], 1]], 2]
```

The result of this code is 2, assuming it is zero for all passed values `to generate`

,

Does anyone know what I am doing wrong or is there a workaround? Or I just ask too much `VoronoiMesh`

?