A Voronoi poset

Details A Voronoi poset A Voronoi poset

1999-05-04

arxiv.org/abs/math/9905018v1

Mathematics

Metric Geometry

14 pages 4 figures

Scientific paper

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.

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