Given a set S of n points in general position, we consider all k-th order
Voronoi diagrams on S, for k=1,...,n, simultaneously. We deduce symmetry
relations for the number of faces, number of vertices and number of circles of
certain orders. These symmetry relations are independent of the position of the
sites in S. As a consequence we show that the reduced Euler characteristic of
the poset of faces equals zero whenever n odd.Comment: 14 pages 4 figure