==== Polyhedral complexes in polymake ==== Polyhedral complexes are contained in the application ''%%fan%%'', so you hanve to switch application to access the full functionality. > application "fan"; To define polyhedral complexes in ''%%polymake%%'', you need to provide an array of input points and a list of polytopes represented as an array of arrays of point indices. > $pc1 = new PolyhedralComplex(POINTS=>[[1,0,0],[1,0,1],[1,1,0],[1,1,1]],INPUT_POLYTOPES=>[[0,1,2],[2,3],[1]]); Since some of the input polytopes may be redundant, you should ask for the ''%%MAXIMAL_POLYTOPES%%''. > print $pc1->MAXIMAL_POLYTOPES; {0 1 2} {2 3} > $pc1->VISUAL; pcom:pc1
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=== Triangulations === Triangulations of polytopes form an important special class of polytopal complexes. In polymake they are objects of type ''%%SimplicialComplex%%'' (and thus belong to the application ''%%topaz%%''). However, it is easy to convert them as follows: > $c=cube(3); > $triangulation=new PolyhedralComplex(VERTICES=>$c->VERTICES,MAXIMAL_POLYTOPES=>$c->TRIANGULATION->FACETS); === Voronoi Diagrams and regular subdivisions === There are separate tutorials for [[voronoi|Voronoi diagrams]] and [[regular_subdivisions|regluar subdivisions]] of point sets.