A three-dimensional Voronoi diagram partitions 3D space into a set of polyhedra linked to sites. Points inside the polyhedron for a site are closer to than to any other site.

This Demonstration lets you look inside a 3D Voronoi diagram using two-dimensional cross sections perpendicular to the axis.

The cross sections are sets of polygons that change with each value of as you drag the slider. The "next site" button takes a cross section at for the next site and shows the site as the point .