Poisson points are depicted as green dots. The blue structure is the Voronoi tessellation / cells. Some cells are randomly colored black. Poisson-Voronoi percolation is now the study of the black connected components.

One black connected component. Thus, each black Voronoi cell shares a face with another black Voronoi cell.

All Voronoi cells that intersect a cube are shown. Each cell is colored red or blue at random.

Points are put independent from another and uniformly on the sphere. Two points are connected if they are nearly antipodal. Here we see a realization with chromatic number 3. So, any two connected points in this drawing do not share a color.