Voronoi Diagrams

This tutorial is probably also available as a Jupyter notebook in the demo folder in the polymake source and on github.

Different versions of this tutorial: latest release, release 3.3, release 3.2, nightly master

Voronoi diagrams are constructed from their sites (given in homogeneous coordinates).

> $VD = new VoronoiPolyhedron(SITES=>[[1,1,1],[1,0,1],[1,-1,1],[1,1,-1],[1,0,-1],[1,-1,-1]]);
> $VD->VISUAL_VORONOI;

Actually, via lifting to the standard paraboloid, Voronoi diagrams are derived from Polytope. That's why they have VERTICES, FACETS, and such.

> print $VD->FACETS;
2 -2 -2 1
1 0 -2 1
2 2 -2 1
2 -2 2 1
1 0 2 1
2 2 2 1
1 0 0 0
    
> print $VD->VERTICES;
0 0 1 2
0 1 0 2
1 1/2 0 -1
0 -1 0 2
0 0 -1 2
1 -1/2 0 -1