# Voronoi diagram with given number of vertices and sites

I want to draw a Voronoi diagram with 9 sites and with

1. no vertex,
2. 1 vertex,
3. 4 vertices, and
4. 7 vertices.

How do I approach this question. The one with no vertex is easy, it can be done by collinear points. What about the others.

A figure for each would be appreciated.

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What have you tried? –  Raphael Nov 19 '12 at 18:21

Conceptually, it is maybe easier to construct a Delaunay triangulation tessalation. The DT is the dual to the Voronoi diagramm, so you want to limit the number of faces to $0,1,4,7$. This can be achieved by placing some of the vertices of the DT on a circle, or by picking the right number of vertices on the convex hull.